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Positivity and higher Teichmüller theoryFeb 08 2018We introduce $\Theta$-positivity, a new notion of positivity in real semisimple Lie groups. The notion of $\Theta$-positivity generalizes at the same time Lusztig's total positivity in split real Lie groups as well as well known concepts of positivity ... More
Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class groupFeb 08 2018These notes are the English version of the paper "Hyperbolicit\'e du graphe des rayons et quasi-morphismes sur un gros groupe modulaire". The mapping class group Gamma of the complement of a Cantor set in the plane arises naturally in dynamics. We show ... More
On characteristic classes of exotic manifold bundlesFeb 07 2018Given a closed simply-connected manifold $M$ of dimension $2n\neq4$, we compare the ring of characteristic classes of smooth oriented bundles with fibre $M$ to the respective ring resulting from replacing $M$ by the connected sum $M\sharp\Sigma$ with ... More
Infinite series in cohomology: attractors and Conley indexFeb 07 2018In this paper we study the cohomological Conley index of arbitrary isolated invariant continua for continuous maps $f \colon U \subseteq \mathbb{R}^d \to \mathbb{R}^d$ by analyzing the topological structure of their unstable manifold. We provide a simple ... More
The monodromy of meromorphic projective structuresFeb 07 2018We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $\mathrm{PGL}_2(\mathbb{C})$ local systems on the associated marked ... More
Up to topological concordance links are strongly quasipositiveFeb 07 2018We generalize an algorithm of Rudolph to establish that every link is topologically concordant to a strongly quasipositive link.
Holomorphic polygons and the bordered Heegaard Floer homology of link complementsFeb 07 2018We describe the construction of an $\mathcal{A}_\infty$ multi-module in terms of counts of holomorphic polygons in a series Heegaard multi-diagrams. We show that this is quasi-isomorphic to the type-A bordered-sutured invariant of a link complement with ... More
Tautological classes and smooth bundles over BSU(2)Feb 06 2018For a Lie group G and a smooth manifold W, we study the difference between smooth actions of G on W and bundles over the classifying space of G with fiber W and structure group Diff(W). In particular, we exhibit smooth manifold bundles over BSU(2) that ... More
Applications of involutive Heegaard Floer homologyFeb 06 2018We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to Stoffregen's ... More
Slopes and signatures of linksFeb 06 2018We define the slope of a colored link in an integral homology sphere, associated to admissible characters on the link group. Away from a certain singular locus, the slope is a rational function which can be regarded as a multivariate generalization of ... More
Topological symmetries of simply-connected four-manifolds and actions of automorphism groups of free groupsFeb 06 2018Let $M$ be a simply connected closed $4$-manifold. It is proved that any (possibly finite) compact Lie group acting effectively and homologically trivially on $M$ by homeomorphisms is an abelian group of rank at most two. As applications, let $\mathrm{Aut}(F_{n})$ ... More
Ascent slicenessFeb 05 2018We introduce the notion of ascent sliceness of virtual knots. A representative of a virtual knot is an embedding $ S^1 \hookrightarrow \Sigma_{g} \times I $, for $ \Sigma_g $ a closed connected oriented surface of genus $ g $; the virtual knot represented ... More
Commutator Subgroups of Virtual and Welded Braid GroupsFeb 05 2018Let $VB_n$, resp. $WB_n$ denote the virtual, resp. welded, braid group on $n$ strands. We study their commutator subgroups $VB_n' = [VB_n, VB_n]$ and, $WB_n' = [WB_n, WB_n]$ respectively. We obtain a set of generators and defining relations for these ... More
All principal congruence link groupsFeb 05 2018In this paper we give a complete enumeration of all the principal congruence link complements in $S^3$, thereby answering a question of W. Thurston.
Burnside groups and $n$-moves for linksJan 30 2018Let $n$ be a positive integer. M. K. Dabkowski and J. H. Przytycki introduced the $n$th Burnside group of links which is preserved by $n$-moves, and proved that for any odd prime $p$ there exist links which are not equivalent to trivial links up to $p$-moves ... More
On Bott-Morse Foliations and their Poisson Structures in Dimension 3Jan 29 2018We show that a Bott-Morse foliation in dimension 3 admits a linear, singular, Poisson structure of rank 2 with Bott-Morse singularities. We provide the Poisson bivectors for each type of singular component, and compute the symplectic forms of the characteristic ... More
Quantum Racah matrices up to level 3 and multicolored link invariantsJan 29 2018This paper is a next step in the project of systematic description of colored knot and link invariants started in previous papers. In this paper, we managed to explicitly find the inclusive Racah matrices, i.e. the whole set of mixing matrices in channels ... More
Trisections of 4-manifolds with BoundaryJan 26 2018Given a handle decomposition of a 4-manifold with boundary, and an open book decomposition of the boundary, we show how to produce a trisection diagram of a trisection of the 4-manifold inducing the given open book. We do this by making the original proof ... More
On a class of immersions of spheres into space forms of nonpositive curvatureJan 25 2018Let $ J $ be an interval and $ M^{n+1} $ be a simply-connected space form of curvature $ -\kappa $, where $ \kappa \geq 0$. If $ J \subset [-\kappa,\kappa] $, then no closed $ n $-manifold can be immersed in $ M $ subject to the restriction that the principal ... More
Knot concordance in homology cobordismsJan 23 2018Let $\widehat{\mathcal{C}}_{\mathbb{Z}}$ denote the group of knots in homology spheres that bound homology balls, modulo smooth concordance in homology cobordisms. Answering a question of Matsumoto, the second author previously showed that the natural ... More
Khovanov homology detects the trefoilsJan 23 2018We prove that Khovanov homology detects the trefoils. Our proof incorporates an array of ideas in Floer homology and contact geometry. It uses open books; the contact invariants we defined in the instanton Floer setting; a bypass exact triangle in sutured ... More
An upper bound on the asymptotic translation lengths on the curve graph and fibered facesJan 20 2018We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold $M$ with $b_1(M) \geq 2$. For a sequence $(\Sigma_n, \psi_n)$ of fibers and ... More
A note on the knot Floer homology of fibered knotsJan 19 2018We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include new proofs of Krcatovich's result that knots with $L$-space surgeries are prime and Hedden and Watson's result that ... More
Normal subgroups of the braid group and the metaconjecture of IvanovJan 16 2018We show that many normal subgroups of the braid group modulo its centre, and of the mapping class group of a sphere with marked points, have the property that their automorphism and abstract commensurator groups are mapping class groups of such spheres. ... More
Homogeneous length functions on groupsJan 11 2018A pseudo-length function defined on an arbitrary group $G = (G,\cdot,e, (\,)^{-1})$ is a map $\ell : G \to [0,+\infty)$ obeying $\ell(e)=0$, the symmetry property $\ell(x^{-1}) = \ell(x)$, and the triangle inequality $\ell(xy) \leqslant \ell(x) + \ell(y)$ ... More
Stability in the homology of Deligne-Mumford compactificationsJan 11 2018Using the the theory of FS^op modules, we study the asymptotic behavior of the homology of $\overline M_{g,n}$, the Deligne--Mumford compactification of the moduli space of curves, for $n >> 0$. An FS^op module is a contravariant functor from the category ... More
Computing rotation numbers in open booksJan 03 2018We give explicit formulas and algorithms for the computation of the rotation number of a nullhomologous Legendrian knot on a page of a contact open book. On the way, we derive new formulas for the computation of the Thurston-Bennequin invariant of such ... More
On the Khovanov Homology of SurgeriesNov 05 2017We show a spectral sequence for the rational Khovanov homology of an oriented link in terms of the rational Khovanov complexes and homologies of the link surgeries along an admissible cut. As a non trivial corollary, we give an explicit splitting formula ... More
Homological stability of topological moduli spacesOct 23 2017Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for the graded ... More
Contact orderability up to conjugationSep 27 2017We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of non-compact contact manifolds, called convex at infinity.
Flows on the PSL(V)-Hitchin componentSep 11 2017Sep 30 2017In this article we define new flows on the Hitchin components for PSL(n,R). Special examples of these flows are associated to simple closed curves on the surface and give generalized twist flows. Other examples, so called eruption flows, are associated ... More
Goldman-Turaev formality from the Knizhnik-Zamolodchikov connectionAug 10 2017For an oriented 2-dimensional manifold $\Sigma$ of genus $g$ with $n$ boundary components the space $\mathbb{C}\pi_1(\Sigma)/[\mathbb{C}\pi_1(\Sigma), \mathbb{C}\pi_1(\Sigma)]$ carries the Goldman-Turaev Lie bialgebra structure defined in terms of intersections ... More
Weinstein manifolds revisitedJul 11 2017Aug 29 2017This is a very biased and incomplete survey of some basic notions, old and new results, as well as open problems concerning Weinstein symplectic manifolds.
Centers of disks in Riemannian manifoldsJun 25 2017We prove the existence of a center, or continuous selection of a point, in the relative interior of $C^1$ embedded $k$-disks in Riemannian $n$-manifolds. If $k\le 3$ the center can be made equivariant with respect to the isometries of the manifold, and ... More
Cyclic hyperbolic Veech groups in finite areaJun 20 2017We prove that there are finite area flat surfaces whose Veech group is an infinite cyclic group consisting of hyperbolic elements
Metric reconstruction via optimal transportJun 15 2017Given a sample of points $X$ in a metric space $M$ and a scale $r>0$, the Vietoris-Rips simplicial complex $\mathrm{VR}(X;r)$ is a standard construction to attempt to recover $M$ from $X$ up to homotopy type. A deficiency of this approach is that $\mathrm{VR}(X;r)$ ... More
Equivariant maps into Anti-de Sitter space and the symplectic geometry of $\mathbb H^2\times \mathbb H^2$May 31 2017Sep 28 2017Given two Fuchsian representations $\rho_l$ and $\rho_r$ of the fundamental group of a closed oriented surface $S$ of genus $\geq 2$, we study the relation between Lagrangian submanifolds of $M_\rho=(\mathbb{H}^2/\rho_l(\pi_1(S)))\times (\mathbb{H}^2/\rho_r(\pi_1(S)))$ ... More
Logarithmic Hennings invariants for restricted quantum sl(2)May 08 2017May 30 2017We construct a Hennings type logarithmic invariant for restricted quantum $\mathfrak{sl}(2)$ at a $2\mathsf{p}$-th root of unity. This quantum group $U$ is not braided, but factorizable. The invariant is defined for a pair: a 3-manifold $M$ and a colored ... More
Differential algebra of cubic planar graphsMay 02 2017May 03 2017In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In addition, ... More
Examples of non-trivial contact mapping classes for overtwisted contact manifolds in all dimensionsApr 24 2017May 19 2017The aim of the article is to construct (infinitely many) examples in all dimensions of contactomorphisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopic to the identity. Hence, overtwisted contact structures ... More
Infinite rank surface cluster algebrasApr 06 2017May 08 2017We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite mutation sequences. ... More
The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problemMar 16 2017In this paper, we describe a surprising link between the theory of the Goldman-Turaev Lie bialgebra on surfaces of genus zero and the Kashiwara-Vergne (KV) problem in Lie theory. Let $\Sigma$ be an oriented 2-dimensional manifold with non-empty boundary ... More
Cosmetic contact surgeries along transverse knots and the knot complement problemMar 16 2017We study cosmetic contact surgeries along transverse knots in the standard contact 3-sphere, i.e. contact surgeries that yield again the standard contact 3-sphere. The main result is that we can exclude non-trivial cosmetic contact surgeries (in sufficiently ... More
Morse structures on partial open books with extendable monodromyFeb 24 2017The first author in recent work with D. Gay developed the notion of a Morse structure on an open book as a tool for studying closed contact 3-manifolds. We extend the notion of Morse structure to extendable partial open books in order to study contact ... More
A splitting theorem for the Seiberg-Witten invariant of a homology $S^1 \times S^3$Feb 14 2017Feb 27 2017We study the Seiberg-Witten invariant $\lambda_{\rm{SW}} (X)$ of smooth spin $4$-manifolds $X$ with integral homology of $S^1\times S^3$ defined by Mrowka, Ruberman, and Saveliev as a signed count of irreducible monopoles amended by an index-theoretic ... More
Competitive division of a mixed mannaFeb 02 2017A mixed manna contains goods (that everyone likes), bads (that everyone dislikes), as well as items that are goods to some agents, but bads or satiated to others. If all items are goods and utility functions are homothetic, concave (and monotone), the ... More
Deforming convex real projective structuresFeb 02 2017Let S be a closed, connected, orientable surface of genus at least 2, and let C(S) denote the deformation space of convex real projective structures S. In this article, we introduce two new flows on C(S), which we call the internal bulging flow and the ... More
A Bayesian Game without epsilon equilibriaJan 27 2017We present a three player Bayesian game for which there is no epsilon equilibria in Borel measurable strategies for small enough epsilon, however there are non-measurable equilibria.
Roots of Dehn twists on nonorientable surfacesJan 02 2017Aug 14 2017Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist t_c about a nonseparating circle c in the mapping class group M(N_g) of a nonorientable surface N_g of genus ... More
On the volume of double twist link cone-manifoldsDec 08 2016We consider the double twist link $J(2m+1, 2n+1)$ which is the two-bridge link corresponding to the continued fraction $(2m+1)-1/(2n+1)$. It is known that $J(2m+1, 2n+1)$ has reducible nonabelian $SL_2(\mathbb{C})$-character variety if and only if $m=n$. ... More
Simple loops on punctured surfaces and boundaries of character varietiesDec 08 2016We prove that every relative moduli space of complex special linear local systems of rank two on a punctured surface is log Calabi-Yau, in that it has a normal projective compactification with anticanonical boundary divisor. We connect this to another ... More
Formation of coalition structures as a non-cooperative game 1: theoryDec 07 2016The paper defines a non-cooperative simultaneous finite game to study coalition structure formation with intra and inter-coalition externalities. The novelty of the game is that the game definition embeds a \textit{coalition structure formation mechanism}. ... More
Unknotted gropes, Whitney towers, and doubly slicing knotsDec 07 2016We study the structure of the exteriors of gropes and Whitney towers in dimension 4, focusing on their fundamental groups. In particular we introduce a notion of unknottedness of gropes and Whitney towers in the 4-sphere. We prove that various modifications ... More
A $q$-series identity via the $\mathfrak{sl}_3$ colored Jones polynomials for the $(2,2m)$-torus linkDec 07 2016The colored Jones polynomial is a $q$-polynomial invariant of links colored by irreducible representations of a simple Lie algebra. A $q$-series called a tail is obtained as the limit of the $\mathfrak{sl}_2$ colored Jones polynomials $\{J_n(K;q)\}_n$ ... More
The first Pontrjagin classes of homotopy complex projective spacesDec 06 2016Let $M^{2n}$ be a closed smooth manifold homotopy equivalent to the complex projective space $\mathbb{C}P(n)$. The purpose of this paper is to show that when $n$ is even, the difference of the first Pontrjagin classes between $M^{2n}$ and $\mathbb{C}P(n)$ ... More
Geometric intersection number of simple closed curves on a surface and symplectic expansions of free groupsDec 06 2016For two oriented simple closed curves on a compact orientable surface with a connected boundary we introduce a simple computation of a value in the first homology group of the surface, which detects in some cases that the geometric intersection number ... More
Homologie Instanton Symplectique : somme connexe, chirurgie entière, et applications induites par cobordismesDec 05 2016Symplectic instanton homology is an invariant for closed oriented three-manifolds, defined by Manolescu and Woodward, which conjecturally corresponds to a symplectic version of a variant of Floer's instanton homology. In this thesis we study the behaviour ... More
Palindromic widths of some free constructionsDec 05 2016In this paper, we consider the palindromic widths in HNN extensions of groups and the amalgamated free products of groups. We show that the palindromic width is infinite in both the cases.
Bounds for entries of $γ$-vectors of flag simplicial spheresDec 04 2016We present some enumerative and structural results for flag homology spheres. For a flag homology sphere $\Delta$, we show that its $\gamma$-vector $\gamma^\Delta=(1,\gamma_1,\gamma_2,\ldots)$ satisfies: \begin{align*} \gamma_j=0,\text{ for all } j>\gamma_1, ... More
Composing generic linearly perturbed mappings and immersions/injectionsDec 04 2016Let $f$ be an immersion of a manifold $N$ into an open subspace $U$ of $\mathbb{R}^m$. Let $F:U\to \mathbb{R}^\ell$ be a mapping. Generally, the composition $F\circ f$ does not necessarily yield a transverse mapping to a given subfiber-bundle of $J^1(N,\mathbb{R}^\ell)$. ... More
On link diagrams that are minimal with respect to Reidemeister moves I and IIDec 02 2016In this paper, a link diagram is said to be minimal if no Reidemeister move I or II can be applied to it to reduce the number of crossings. We show that for an arbitrary diagram D of a link without a trivial split component, a minimal diagram obtained ... More
Non-manifold monodromy spaces of branched coverings between manifoldsDec 02 2016By a construction of Berstein and Edmonds every proper branched cover f between manifolds is a factor of a branched covering orbit map from a locally connected and locally compact Hausdorff space called the monodromy space of f to the target manifold. ... More
Immersions of S^1 (and graphs) in surfacesDec 01 2016Dec 05 2016We obtain a classification of immersions $f$ of $S^1$ in a $2$-manifold $M$ in terms of elementary invariants: the parity $S(f)$ of the number of double points of a generic $C^1$-approximation of $f$, and the turning number $T(f,o)$ of $\phi_o\bar f$, ... More
Immersions of S^1 (and graphs) in surfacesDec 01 2016We obtain a classification of immersions $f$ of $S^1$ in a $2$-manifold $M$ in terms of simple geometric invariants: the parity $S(f)$ of the number of double points of $f$ and the turning number $T(f,o)$ of $\phi_o\bar f$, where $\bar f$ is a lift of ... More
Factorization of differential expansion for non-rectangular representationsDec 01 2016Factorization of the differential expansion coefficients for HOMFLY-PT polynomials of double braids, discovered in arXiv:1606.06015 in the case of rectangular representations $R$, is extended to the first non-rectangular representations $R=[2,1]$ and ... More
Factorization of differential expansion for non-rectangular representationsDec 01 2016Dec 05 2016Factorization of the differential expansion coefficients for HOMFLY-PT polynomials of double braids, discovered in arXiv:1606.06015 in the case of rectangular representations $R$, is extended to the first non-rectangular representations $R=[2,1]$ and ... More
Self-similar sets, simple augmented trees, and their Lipschitz equivalenceDec 01 2016Given an iterated function system (IFS) of contractive similitudes, the theory of Gromov hyperbolic graph on the IFS has been established recently. In the paper, we introduce a notion of simple augmented tree which is a Gromov hyperbolic graph. By generalizing ... More
Pro-$p$ subgroups of profinite completions of 3-manifold groupsDec 01 2016We completely describe the finitely generated pro-$p$ subgroups of the profinite completion of the fundamental group of an arbitrary $3$-manifold. We also prove a pro-$p$ analogue of the main theorem of Bass--Serre theory for finitely generated pro-$p$ ... More
Equilibrium Computation in Atomic Splittable Singleton Congestion GamesDec 01 2016We devise the first polynomial time algorithm computing a pure Nash equilibrium for atomic splittable congestion games with singleton strategies and player-specific affine cost functions. Our algorithm is purely combinatorial and computes the exact equilibrium ... More
Menu-Based Pricing for Charging of Electric Vehicles with Vehicle-to-Grid ServiceDec 01 2016The paper considers a bidirectional power flow model of the electric vehicles (EVs) in a charging station. The EVs can inject energies by discharging via a Vehicle-to-Grid (V2G) service which can enhance the profits of the charging station. However, frequent ... More
On the moduli space of flat symplectic surface bundlesNov 30 2016In this paper, we prove homological stability of symplectomorphisms and extended hamiltonians of surfaces made discrete. We construct an isomorphism from the stable homology group of symplectomorphisms and extended Hamiltonians of surfaces to the homology ... More
Linking Numbers in Three-ManifoldsNov 30 2016We give an explicit algorithm for computing linking numbers between curves in an irregular dihedral $p$-fold branched cover of $S^3$. This work extends a combinatorial algorithm by Perko which computes the linking number between the branch curves in the ... More
Is Non-Neutrality Profitable for the Stakeholders of the Internet Market?Nov 30 2016We consider a system in which there exists two ISPs, one "big" Content Provider (CP), and a continuum of End-Users (EUs). One of the ISPs is neutral and the other is non-neutral. We consider that the CP can differentiate between ISPs by controlling the ... More
A Majoritarian Representative Voting SystemNov 30 2016We present an alternative voting system that aims at bridging the gap between proportional representative systems and majoritarian, single winner election systems. The system lets people vote for multiple parties, but then assigns each ballot to a single ... More
Alternating maps on Hatcher-Thurston graphsNov 30 2016Let $S_{1}$ and $S_{2}$ be connected orientable surfaces of genus $g_{1}, g_{2} \geq 3$, $n_{1},n_{2} \geq 0$ punctures, and empty boundary. Let also $\varphi: \mathcal{HT}(S_{1}) \rightarrow \mathcal{HT}(S_{2})$ be an edge-preserving alternating map ... More
A Functorial Symplectic Instanton Homology via Traceless Character VarietiesNov 29 2016Using ideas pioneered by Wehrheim and Woodward, we associate to any closed, oriented $3$-manifold $Y$ a finitely generated abelian group $\mathrm{SI}(Y)$ obtained from (quilted) Lagrangian Floer homology in a certain moduli space of $\mathrm{SU}(2)$-representations ... More
Minimal foliations by hyperbolic surfaces on 3-manifoldsNov 29 2016We describe several methods to construct minimal foliations by hyperbolic surfaces on closed 3-manifolds, and discuss the properties of the examples thus obtained. These methods can roughly be grouped into cut-and-paste constructions, deformation of fibrations ... More
Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theoryNov 29 2016We explain an elementary, topological construction of the Springer representation on the homology of (topological) Springer fibers of types C and D in the case of nilpotent endomorphisms with two Jordan blocks. The Weyl group action and the component ... More
A Reputation-Based Contract for Repeated Crowdsensing with Costly VerificationNov 29 2016We study a setup in which a system operator hires a sensor to exert costly effort to collect accurate measurements of a value of interest over time. At each time, the sensor is asked to report his observation to the operator, and is compensated based ... More
Graphs immersions to the projective planeNov 29 2016Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
Maximum a posteriori learning in demand competition gamesNov 28 2016We consider an inventory competition game between two firms. The question we address is this: If players do not know the opponent's action and opponent's utility function can they learn to play the Nash policy in a repeated game by observing their own ... More
$τ$-invariants for knots in rational homology spheresNov 28 2016Ozsv\'ath and Szab\'o used the knot filtration on $\hat{CF}(S^3)$ to define the $\tau$-invariant for knots in $S^3$. In this article we generalize their construction and define a collection of invariants $\{\tau_\mathfrak{s}(Y,K)\}_{\mathfrak{s}\in\S(Y)}$ ... More
Kodaira fibrations, Kähler groups, and finiteness propertiesNov 28 2016We construct classes of K\"ahler groups that do not have finite classifying spaces and are not commensurable to subdirect products of surface groups. Each of these groups is the fundamental group of the generic fibre of a regular holomorphic map from ... More
On Kahler extensions of abelian groupsNov 28 2016We show that any Kahler extension of a finitely generated abelian group by a surface group of genus g at least 2 is virtually a product. Conversely, we prove that any homomorphism of an even rank, finitely generated abelian group into the genus g mapping ... More
Alexander type invariants of tanglesNov 28 2016We study generalizations of a classical link invariant -- the multivariable Alexander polynomial -- to tangles. The starting point is Archibald's tMVA invariant for virtual tangles which lives in the setting of circuit algebras, and whose target space ... More
Satellites and concordance of knots in 3-manifoldsNov 28 2016Given a 3-manifold $Y$ and a free homotopy class in $[S^1,Y]$, we investigate the set of topological concordance classes of knots in $Y \times [0,1]$ representing the given homotopy class. The concordance group of knots in the 3-sphere acts on this set. ... More
Spaces of curves with constrained curvature on hyperbolic surfacesNov 28 2016Let $ S $ be a hyperbolic surface. We investigate the topology of the space of all curves on $ S $ which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval $ (\kappa_1,\kappa_2) $. These ... More
On the global rigidity of sphere packings on 3-dimensional manifoldsNov 27 2016In this paper, we prove the global rigidity of sphere packings on 3-dimensional triangulated manifolds, which was conjectured by Cooper and Rivin in \cite{CR}. This is an analogue of the rigidity part of Andreev-Thurston Theorem in three dimension. We ... More
Phragmén's and Thiele's election methodsNov 27 2016The election methods introduced in 1894--1895 by Phragm\'en and Thiele, and their somewhat later versions for ordered (ranked) ballots, are discussed in detail. The paper includes definitions and examples and discussion of whether the methods satisfy ... More
Open-closed modular operads, Cardy condition and string field theoryNov 26 2016We prove that the modular operad of diffeomorphism classes of Riemann surfaces with both `open' and `closed' boundary components, in the sense of string field theory, is the modular completion of its genus 0 part quotiented by the Cardy condition. We ... More
Truthful Spectrum Auction for Efficient Anti-Jamming in Cognitive Radio NetworksNov 26 2016One significant challenge in cognitive radio networks is to design a framework in which the selfish secondary users are obliged to interact with each other truthfully. Moreover, due to the vulnerability of these networks against jamming attacks, designing ... More
Reduction for $SL(3)$ pre-buildingsNov 26 2016Given an $SL(3)$ spectral curve over a simply connected Riemann surface, we describe in detail the reduction steps necessary to construct the core of a pre-building with versal harmonic map whose differential is given by the spectral curve.
Homological dimension and dimensional full-valuednessNov 25 2016There are different definitions of homological dimension of metric compacta involving either \v{C}ech homology or exact (Steenrod) homology. In this paper we investigate the relation between these homological dimensions with respect to different groups. ... More
Edge-preserving maps of curve graphsNov 25 2016Suppose $S_{1}$ and $S_{2}$ are orientable surfaces of finite topological type such that $S_{1}$ has genus at least $3$ and the complexity of $S_{1}$ is an upper bound of the complexity of $S_{2}$. Let $\varphi : \mathcal{C}(S_{1}) \rightarrow \mathcal{C}(S_{2})$ ... More
Cauchy-Compact flat spacetimes with BTZ singularitiesNov 24 2016The zoology of singularities for Lorentzian manifold is slightly more complicated than for Riemannian manifolds. Our present work study Cauchy-compact globally hyperbolic singular flat spacetimes with extreme BTZ-like singular lines. We use the notion ... More
Topological Aspects of Quantum EntanglementNov 24 2016Kauffman and Lomonaco introduced the idea of understanding quantum entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In the work of Alagic, Jarret and ... More
Classification and Models of Simply-connected Trivalent $2$-dimensional StratifoldsNov 23 2016Trivalent $2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where three sheets meet. We obtain a classification of $1$-connected $2$-stratifolds in terms of their associated labeled graphs and develop ... More
Exhaustion of the curve graph via rigid expansionsNov 23 2016For an orientable surface $S$ of finite topological type with genus $g \geq 3$, we construct a finite set of curves whose union of iterated rigid expansions is the curve graph of $S$. The set constructed, and the method of rigid expansion, are closely ... More
Effective divisors in $\overline{\mathcal{M}}_{g,n}$ from abelian differentialsNov 23 2016We compute many new classes of effective divisors in $\overline{\mathcal{M}}_{g,n}$ coming from the strata of abelian differentials and efficiently reproduce many known results obtained by alternate methods. Our method utilises maps between moduli spaces ... More
On the decategorification of Ozsváth and Szabó's bordered theory for knot Floer homologyNov 23 2016We relate decategorifications of Ozsv\'ath-Szab\'o's new bordered theory for knot Floer homology to representations of $\mathcal{U}_q(\mathfrak{gl}(1|1))$. Specifically, we consider two subalgebras $\mathcal{C}_r(n,\mathcal{S})$ and $\mathcal{C}_l(n,\mathcal{S})$ ... More