Latest in math.gt

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0-Concordance of 2-knotsJul 15 2019In this paper we investigate the 0-concordance classes of 2-knots in $S^4$, an equivalence relation that is related to understanding smooth structures on 4-manifolds. Using Rochlin's invariant, and invariants arising from Heegaard-Floer homology, we will ... More
Labels instead of coefficients: a label bracket which dominates the Jones polynomial, the Kuperberg bracket, and the normalised arrow polynomialJul 15 2019In the present paper we develop a picture formalism which gives rise to an invariant that dominates several known invariants of classical and virtual knots: the Jones polynomial, the Kuperberg bracket, and the normalized arrow polynomial.
Legendrian Hopf linksJul 15 2019We completely classify Legendrian realisations of the Hopf link, up to coarse equivalence, in the 3-sphere with any contact structure.
Envelopes in Outer SpaceJul 15 2019We study the geometry of Outer Space $CV_n$ in regard of the asymmetric Lipschitz metric via envelopes, that is the set of all geodesics between two points. In the simplicial structure of $CV_n$ the envelopes are polytopes. We construct a piecewise unique ... More
Square-integrability of the Mirzakhani function and statistics of simple closed geodesics on hyperbolic surfacesJul 14 2019Given integers $g,n \geq 0$ satisfying $2-2g-n < 0$, let $\mathcal{M}_{g,n}$ be the moduli space of connected, oriented, complete, finite area hyperbolic surfaces of genus $g$ with $n$ cusps. We study the global behavior of the Mirzakhani function $B ... More
Metric Thickenings, Borsuk-Ulam Theorems, and OrbitopesJul 14 2019Thickenings of a metric space capture local geometric properties of the space. Here we exhibit applications of lower bounding the topology of thickenings of the circle and more generally the sphere. We explain interconnections with the geometry of circle ... More
Trees, dendrites, and the Cannon-Thurston mapJul 14 2019When 1 -> H -> G -> Q -> 1 is a short exact sequence of three infinite, word-hyperbolic groups, Mahan Mitra (Mj) has shown that the inclusion map from H to G extends continuously to a map between the Gromov boundaries of H and G. This boundary map is ... More
Trees, length spectra for rational maps via barycentric extensions and Berkovich spacesJul 14 2019In this paper, we study the dynamics of degenerating sequences of rational maps on Riemann sphere $\hat{\mathbb{C}}$ using $\mathbb{R}$-trees. Given a sequence of degenerating rational maps, we give two constructions for limiting dynamics on $\mathbb{R}$-trees: ... More
Coloring invariants of knots and links are often intractableJul 13 2019Let $G$ be a nonabelian, simple group with a nontrivial conjugacy class $C \subseteq G$. Let $K$ be a diagram of an oriented knot in $S^3$, thought of as computational input. We show that for each such $G$ and $C$, the problem of counting homomorphisms ... More
Finiteness and infiniteness results for Torelli groups of (hyper-)Kähler manifoldsJul 12 2019The Torelli group $\mathcal T(X)$ of a closed smooth manifold $X$ is the subgroup of the mapping class group $\pi_0(\mathrm{Diff}^+(X))$ consisting of elements which act trivially on the integral cohomology of $X$. In this note we give counterexamples ... More
A construction of pseudo-Anosov homeomorphisms using positive twistsJul 11 2019We introduce a construction of pseudo-Anosov homeomorphisms on n-times punctured spheres and surfaces with higher genus using only sufficiently many positive half-twists. These constructions can produce explicit examples of pseudo-Anosov maps with various ... More
Minimax Theorems for Finite Blocklength Lossy Joint Source-Channel Coding over an AVCJul 11 2019Motivated by applications in the security of cyber-physical systems, we pose the finite blocklength communication problem in the presence of a jammer as a zero-sum game between the encoder-decoder team and the jammer, by allowing the communicating team ... More
The dual volume of quasi-Fuchsian manifolds and the Weil-Petersson distanceJul 10 2019Making use of the dual Bonahon-Schl\"afli formula, we prove that the dual volume of the convex core of a quasi-Fuchsian manifold $M$ is bounded by an explicit constant, depending only on the topology of $M$, times the Weil-Petersson distance between the ... More
Hyperbolic links are not genericJul 09 2019We show that if $K$ is a nontrivial knot then the proportion of satellites of $K$ among all of the prime non-split links of $n$ or fewer crossings does not converge to $0$ as $n$ approaches infinity. This implies in particular that the proportion of hyperbolic ... More
Finite Regret and Cycles with Fixed Step-Size via Alternating Gradient Descent-AscentJul 09 2019Gradient descent is arguably one of the most popular online optimization methods with a wide array of applications. However, the standard implementation where agents simultaneously update their strategies yields several undesirable properties; strategies ... More
Commensurators of thin normal subgroupsJul 09 2019We give an affirmative answer to many cases of a question due to Shalom, which asks if the commensurator of a thin subgroup of a Lie group is discrete. In this paper, let $K<\Gamma<G$ be an infinite normal subgroup of an arithmetic lattice $\Gamma$ in ... More
Constraints on families of smooth 4-manifolds from Bauer-Furuta invariantsJul 09 2019We obtain constraints on the topology of families of smooth $4$-manifolds arising from a finite dimensional approximation of the families Seiberg-Witten monopole map. Amongst other results these constraints include a families generalisation of Donaldson's ... More
Representations of surface groups with universally finite mapping class group orbitJul 09 2019Let $\Sigma_{g,n}$ be the orientable genus $g$ surface with $n$ punctures, such that $2-2g-n<0$, and let $\Gamma_{g,n}$ be its fundamental group. Let $$\rho: \Gamma_{g, n}\to GL_m(\mathbb{C})$$ be a representation. Suppose that for each finite covering ... More
Arithmetic topology of 4-manifoldsJul 08 2019We construct a functor from the smooth 4-dimensional manifolds to the hyper-algebraic number fields, i.e. fields with a non-commutative multiplication. It is proved that that the simply connected 4-manifolds correspond to the abelian extensions. As a ... More
A Note on Alexander Polynomials of 2-Bridge LinksJul 08 2019A formula for the Alexander polynomial of a 2-bridge knot or link given by Hartley and also by Minkus has a beautiful interpretation as a walk on the integers. We extend this to the 2-variable Alexander polynomial of a 2-bridge link, obtaining a formula ... More
In search of stable geometric structuresJul 08 2019We will look for stable structures in four situations and discuss what is known and unknown.
Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifoldsJul 08 2019We study the twisted index of 4d $\mathcal{N}$ = 2 class S theories on a closed hyperbolic 3-manifold $M_3$. Via 6d picture, the index can be written in terms of simple topological invariants and analytic torsions twisted by irreducible flat connections ... More
JT Gravity and the Ensembles of Random Matrix TheoryJul 07 2019We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between ... More
Hairy Cantor setsJul 07 2019We introduce a topological object, called hairy Cantor set, which in many ways enjoys the universal features of objects like Jordan curve, Cantor set, Cantor bouquet, hairy Jordan curve, etc. We give an axiomatic characterisation of hairy Cantor sets, ... More
Manifolds homotopy equivalent to certain torus bundles over lens spacesJul 07 2019We compute the topological simple structure set of closed manifolds which occur as total spaces of flat bundles over lens spaces S^l/(Z/p) with fiber an n-dimensjional torus T^n for an odd prime p and l greater or equal to 3, provided that the induced ... More
Quasi-homomorphisms on mapping class groups vanishing on a handlebody groupJul 07 2019We construct infinitely many linearly independent quasi-homomorphisms on the mapping class group of a Riemann surface with genus at least two which vanish on a handlebody subgroup. As a corollary, we disprove a conjecture of Reznikov on bounded width ... More
A flat torus theorem for convex co-compact actions of projective linear groupsJul 07 2019In this paper, we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish an analogue of the well known flat torus theorem for ${\rm CAT}(0)$ ... More
Symmetries of Spatial Graphs in Homology SpheresJul 06 2019This paper explores the relationship between symmetries of spatial graphs in $S^3$ and symmetries of spatial graphs in homology $3$-spheres and other $3$-manifolds. We prove that for any $3$-connected graph $G$, an automorphism $\sigma$ is induced by ... More
Reconstructing maps out of groupsJul 05 2019We show that, in many situations, a homeomorphism $f$ of a manifold $M$ may be recovered from the (marked) isomorphism class of a finitely generated group of homeomorphisms containing $f$. As an application, we relate the notions of {\em critical regularity} ... More
Quantum Enhancements via Tribracket BracketsJul 05 2019We enhance the tribracket counting invariant with \textit{tribracket brackets}, skein invariants of tribracket-colored oriented knots and links analogously to biquandle brackets. This infinite family of invariants includes the classical quantum invariants ... More
Coxeter groups and meridional rank of linksJul 05 2019We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These are substantial generalizations of pretzel links and two-bridge links. Lower bounds on meridional rank are obtained ... More
On the sheaf-theoretic SL(2,C) Casson-Lin invariantJul 04 2019We prove that the ($\tau$-weighted, sheaf-theoretic) SL(2,C) Casson-Lin invariant introduced by Manolescu and the first author in [CM19] is generically independent of $\tau$ and additive under connected sums of knots in integral homology 3-spheres. This ... More
Degree theory for orbifoldsJul 04 2019In [3] Borzellino and Brunsden started to develop an elementary differential topology theory for orbifolds. In this paper we carry on their project by defining a mapping degree for proper maps between orbifolds, which counts preimages of regular values ... More
Borel invariant for Zimmer cocycles of 3-manifold groupsJul 04 2019Let $\Gamma$ be a non-uniform lattice of $\text{PSL}(2,\mathbb{C})$. Given any representation $\rho:\Gamma \rightarrow \text{PSL}(n,\mathbb{C})$ we can define a numerical invariant $\beta_n(\rho)$, called Borel invariant, which remains constant along ... More
Geometric Moves relate geometric triangulationsJul 04 2019We show that geometric triangulations of a compact hyperbolic, spherical or Euclidean manifold are related by geometric Pachner moves.
Technical report for "Virtual Energy Storage Sharing and Capacity Allocation"Jul 03 2019Energy storage can play an important role in energy management of end users. To promote an efficient utilization of energy storage, we develop a novel business model to enable virtual storage sharing among a group of users. Specifically, a storage aggregator ... More
Technical report for "Virtual Energy Storage Sharing and Capacity Allocation"Jul 03 2019Jul 07 2019Energy storage can play an important role in energy management of end users. To promote an efficient utilization of energy storage, we develop a novel business model to enable virtual storage sharing among a group of users. Specifically, a storage aggregator ... More
Pricing in Resource Allocation Games Based on Duality GapsJul 03 2019We consider a basic resource allocation game, where the players' strategy spaces are subsets of $\mathbb{R}^m$ and cost/utility functions are parameterized by some common vector $u$ and, otherwise, only depend on the own strategy choice. A strategy of ... More
Quantum groups and braiding operators in quantum Teichmüller theoryJul 03 2019We show that the stated skein algebra of a disc with two punctures on its boundary and one inner puncture has a natural structure of Hopf algebra closely related to a construction of Bigelow. Its image through the quantum trace map is a Hopf algebra very ... More
Generalized Bott-Cattaneo-Rossi invariants of high-dimensional long knotsJul 03 2019Bott, Cattaneo and Rossi defined invariants of long knots $\mathbb R^n \hookrightarrow \mathbb R^{n+2}$ as combinations of configuration space integrals. Here, we give a more flexible definition of these invariants. Our definition allows us to interpret ... More
On the complexity of cusped non-hyperbolicityJul 02 2019We show that the problem of showing that a cusped 3-manifold $M$ is not hyperbolic is in NP, assuming $S^3$ recognition is in coNP. Our key contributions are a certificate that a manifold is $\mathbb{T}^2 \times I$ and a certificate that an irreducible ... More
Simplicial complexity of surface groups and systolic areaJul 02 2019The simplicial complexity is an invariant for finitely presentable groups that was recently introduced by Babenko, Balacheff and Bulteau to study systolic area. The simplicial complexity $\kappa(G)$ was proved to be a good approximation of the systolic ... More
Stratification by itineraries of spaces of locally convex curvesJul 02 2019The homotopy type of spaces of locally convex curves with fixed endpoints in $Spin_{n+1}$, the universal covering the orthogonal group $SO_{n+1}$ for $n \ge 2$, has been determined for $n=2$ but is in general not known. The results in this paper have ... More
The quantum trace as a quantum non-abelianization mapJul 02 2019We prove that the balanced Chekhov-Fock algebra of a punctured triangulated surface is isomorphic to a skein algebra which is a deformation of the algebra of regular functions of some abelian character variety. We first deduce from this observation a ... More
Equivariant instanton homologyJul 01 2019We define four versions of equivariant instanton Floer homology ($I^+, I^-, I^\infty$ and $\widetilde I$) for a class of 3-manifolds and $SO(3)$-bundles over them including all rational homology spheres. These versions are analogous to the four flavors ... More
Taut foliations from double-diamond replacementsJul 01 2019A 3-manifold is foliar if it supports a codimension-one co-oriented taut foliation. Suppose $M$ is an oriented 3-manifold with connected boundary a torus, and suppose $M$ contains a properly embedded, compact, oriented, surface $R$ with a single boundary ... More
Cardinal-indexed classifying spaces for families of subgroups of any topological groupJul 01 2019Any $G$-space isovariantly or approximately covered by tubes is the pullback of a classifying space indexed by the orbit types of the tubes and the cardinality of the cover.
Instanton Floer homology for sutured manifolds with tanglesJul 01 2019We prove an excision theorem for the singular instanton Floer homology that allows the excision surfaces to intersect the singular locus. This is an extension of the non-singular excision theorem by Kronheimer and Mrowka and the genus-zero singular excision ... More
Colored UnlinkingJun 29 2019In links with two components there are three different types of crossings: self-crossings in the first component, self crossings in the second component, and crossings between components. In this paper we examine the minimum number of crossing changes ... More
Multistability and regime shifts in microbial communities explained by competition for essential nutrientsJun 29 2019Microbial communities routinely have several possible species compositions or community states observed for the same environmental parameters. Changes in these parameters can trigger abrupt and persistent transitions (regime shifts) between such community ... More
Neck-Pinching of $CP^1$-structures in the PSL(2,C)-character varietyJun 28 2019Jul 02 2019Let S be a closed oriented surface of genus at least two. We consider a path of $CP^1$-structures $C_t$ on S leaving every compact subset in the deformation space of (marked) $CP^1$-structures on S, such that its holonomy converges in the PSL(2, C)-character ... More
BPS Invariants for 3-Manifolds at Rational Level $K$Jun 28 2019We consider the Witten-Reshetikhin-Turaev invariants or Chern-Simons partition function at or around roots of unity $q=e^{2\pi i \frac{1}{K}}$ with rational level $K=\frac{r}{s}$ where $r$ and $s$ are coprime integers. From the exact expression for the ... More
Fundamental groups and path lifting for algebraic varietiesJun 27 2019We study 3 basic questions about fundamental groups of algebraic varieties. For a morphism, is being surjective on $\pi_1$ preserved by base change? What is the connection between openness in the Zariski and in the Euclidean topologies? Which morphisms ... More
Tight fibred knots without L-space surgeriesJun 27 2019We show there exist infinitely many knots of every fixed genus $g\geq 2$ which do not admit surgery to an L-space, despite resembling algebraic knots and L-space knots in general: they are algebraically concordant to the torus knot $T(2,2g+1)$ of the ... More
Homology spheres and property RJun 26 2019We present infinitely many homology spheres which contain two distinct knots whose 0-surgeries are $S^1 \times S^2$. This resolves a question posed by Kirby and Melvin from 1978.
Geometry on all prime Three ManifoldsJun 26 2019The point of this work is to construct geometric structures on the oriented closed prime three manifolds that don't at present already have them. One knows these compound prime three manifolds, have canonically up to deformation from the identity, incompressible ... More
Higher depth quantum modular forms and plumbed $3$-manifoldsJun 25 2019In this paper we study new invariants $\widehat{Z}_{\boldsymbol{a}}(q)$ attached to plumbed $3$-manifolds that were introduced by Gukov, Pei, Putrov, and Vafa. These remarkable $q$-series at radial limits conjecturally compute WRT invariants of the corresponding ... More
Asymptotically Moebius maps and rigidity for the hyperbolic planeJun 25 2019Let $S$ be a rank-one symmetric space of non-compact type and let $X$ be a $\text{CAT}(-1)$ space. A well-known result by Bourdon states that if a topological embedding $\varphi: \partial_\infty S \rightarrow \partial_\infty X$ respects cross ratios, ... More
A lift of the Seiberg-Witten equations to Kaluza-Klein 5-manifoldsJun 24 2019Jul 01 2019We consider Riemannian 4-manifolds X with a Spin^c-structure and a suitable circle bundle Y over X such that the Spin^c-structure on X lifts to a spin structure on Y. With respect to these structures a spinor on X lifts to an untwisted spinor on Y and ... More
A lift of the Seiberg-Witten equations to Kaluza-Klein 5-manifoldsJun 24 2019We consider Riemannian 4-manifolds X with a Spin^c-structure and a suitable circle bundle Y over X such that the Spin^c-structure on X lifts to a spin structure on Y. With respect to these structures a spinor on X lifts to an untwisted spinor on Y and ... More
Topology of leaves for minimal laminations by hyperbolic surfacesJun 24 2019We construct minimal laminations by hyperbolic surfaces whose generic leaf is a disk and contain any prescribed family of surfaces and with a precise control of the topologies of the surfaces that appear. The laminations are constructed via towers of ... More
Pentad and triangular structures behind the Racah matricesJun 24 2019Somewhat unexpectedly, the study of the family of twisted knots revealed a hidden structure behind exclusive Racah matrices $\bar S$, which control non-associativity of the representation product in a peculiar channel $R\otimes \bar R \otimes R \longrightarrow ... More
Random subgroups, automorphisms, splittingsJun 23 2019We show that, if $H$ is a random subgroup of a finitely generated free group $F_k$, only inner automorphisms of $F_k$ may leave $H$ invariant. A similar result holds for random subgroups of toral relatively hyperbolic groups, more generally of groups ... More
Topological constraints for Stein fillings of tight structures on lens spacesJun 21 2019In this article we give a sharp upper bound on the possible values of the Euler characteristic for a minimal symplectic filling of a tight contact structure on a lens space. This estimate is obtained by looking at the topology of the spaces involved, ... More
Problem on Mutant Pairs of Hyperbolic PolyhedraJun 20 2019We present a notion of mutation of hyperbolic polyhedra, analogous to mutation in knot theory, and then present a general question about commensurability of mutant pairs of polyhedra. We motivate that question with several concrete examples of mutant ... More
Compactness and generic finiteness for free boundary minimal hypersurfaces (II)Jun 20 2019Given a compact Riemannian manifold with boundary, we prove that the limit of a sequence of embedded, almost properly embedded free boundary minimal hypersurfaces, with uniform area and Morse index upper bound, always inherits a non-trivial Jacobi field. ... More
On bounded index property for products of aspherical polyhedraJun 20 2019A compact polyhedron $X$ is said to have the Bounded Index Property for Homotopy Equivalence (BIPHE) if there is a finite bound $\mathcal{B}$ such that for any homotopy equivalence $f:X\rightarrow X$ and any fixed point class $\mathbf{F}$ of $f$, the ... More
The effect of link Dehn surgery on the Thurston normJun 20 2019Let $L$ be an $n$-component link ($n>1$) with pairwise nonzero linking numbers in a rational homology $3$-sphere $Y$. Assume the link complement $X:=Y\setminus\nu(L)$ has nondegenerate Thurston norm. In this paper, we study when a Thurston norm-minimizing ... More
The effect of link Dehn surgery on the Thurston normJun 20 2019Jun 29 2019Let $L$ be an $n$-component link ($n>1$) with pairwise nonzero linking numbers in a rational homology $3$-sphere $Y$. Assume the link complement $X:=Y\setminus\nu(L)$ has nondegenerate Thurston norm. In this paper, we study when a Thurston norm-minimizing ... More
Chaos and integrability in SL(2,R)-geometryJun 19 2019The integrability of the geodesic flow on the three-folds $\mathcal M^3$ admitting $SL(2,\mathbb R)$-geometry in Thurston's sense is investigated. The main examples are the quotients $\mathcal M^3_\Gamma=\Gamma\backslash PSL(2,\mathbb R)$, where $\Gamma ... More
A Bauer-Furuta type refinement of Kronheimer-Mrowka's invariant for 4-manifolds with contact boundaryJun 19 2019Kronheimer and Mrowka constructed a variant of Seiberg-Witten invariants for a 4-manifold $X$ with contact boundary in 1997. Using Furuta's finite dimensional approximation, we refine this invariant in the case $H^1(X, \partial X; \mathbb{R})=0$.
A Bauer-Furuta type refinement of Kronheimer-Mrowka's invariant for 4-manifolds with contact boundaryJun 19 2019Jun 25 2019Kronheimer and Mrowka constructed a variant of Seiberg-Witten invariants for a 4-manifold $X$ with contact boundary in 1997. Using Furuta's finite dimensional approximation, we refine this invariant in the case $H^1(X, \partial X; \mathbb{R})=0$.
A cell decomposition of the Fulton MacPherson operadJun 18 2019We construct a regular cellular decomposition of the Fulton MacPherson operad $FM_2$ that is compatible with the operad composition. The cells are indexed by trees with edges of two colors and vertices labelled by cells of the cacti operad. This answers ... More
Recognizing topological polynomials by lifting treesJun 18 2019We give a simple geometric algorithm that can be used to determine whether or not a post-critically finite topological polynomial is Thurston equivalent to a polynomial. If it is, the algorithm produces the Hubbard tree for the polynomial, hence determining ... More
The Powell Conjecture and reducing sphere complexesJun 18 2019The Powell Conjecture offers a finite generating set for the genus $g$ Goeritz group, the group of automorphisms of $S^3$ that preserve a genus $g$ Heegaard surface $\Sigma_g$, generalizing a classical result of Goeritz in the case $g=2$. We study the ... More
Aggregate Play and Welfare in Strategic Interactions on NetworksJun 18 2019In recent work by Bramoull\'{e} and Kranton, a model for the provision of public goods on a network was presented and relations between equilibria of such a game and properties of the network were established. This model was further extended to include ... More
Entropy and codimension bounds for generic singularitiesJun 18 2019Jul 10 2019We show that all closed $2$-dimensional singularities for higher codimension mean curvature flow that cannot be perturbed away have uniform entropy bounds and lie in a linear subspace of small dimension. The entropy and dimension of the subspace are both ... More
Entropy and codimension bounds for generic singularitiesJun 18 2019We show that all closed $2$-dimensional singularities for higher codimension mean curvature flow that cannot be perturbed away have uniform entropy bounds and lie in a linear subspace of small dimension. The entropy and dimension of the subspace are both ... More
Holomorphic one-forms without zeros on threefoldsJun 18 2019We show that a smooth complex projective threefold admits a holomorphic one-form without zeros if and only if the underlying real 6-manifold fibres smoothly over the circle, and we give a complete classification of all threefolds with that property. Our ... More
Zeros of holomorphic one-forms and topology of Kähler manifoldsJun 18 2019A conjecture of Kotschick predicts that a compact K\"ahler manifold $X$ fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. ... More
Masur-Veech volume of the gothic locusJun 18 2019We calculate the Masur-Veech volume of the gothic locus $\mathcal{G}$ in the stratum $\mathcal{H}(2^{3})$ of genus four. Our method is based on the use of the formulae for the Euler characteristics of gothic Teichm\"{u}ller curves to determine the number ... More
On a generalization of Inoue and Oeljeklaus-Toma manifoldsJun 18 2019In this paper we construct a family of complex analytic manifolds that generalize Inoue surfaces and Oeljeklaus-Toma manifolds. To a matrix $M$ in $SL(N,\mathbb{Z})$ satisfying some mild conditions on its characteristic polynomial we associate a manifold ... More
Cusp transitivity in hyperbolic 3-manifoldsJun 17 2019Let $M$ be a cusped finite-volume hyperbolic three-manifold with isometry group $G$. Then $G$ induces a $k$-transitive action by permutation on the cusps of $M$ for some integer $k\ge 0$. Generically $G$ is trivial and $k=0$, but $k>0$ does occur in special ... More
Local topological recursion governs the enumeration of lattice points in $\overline{\mathcal M}_{g,n}$Jun 17 2019The second author and Norbury initiated the enumeration of lattice points in the Deligne-Mumford compactifications of moduli spaces of curves. They showed that the enumeration may be expressed in terms of polynomials, whose top and bottom degree coefficients ... More
Heegaard Floer homology and cosmetic surgeries in $S^3$Jun 16 2019If a knot $K$ in $S^3$ admits a pair of truly cosmetic surgeries, we show that the surgery slopes are $\pm 2$ or $\pm 1/q$ for some $q$. Moreover, in the former case the genus of $K$ must be two, and in the latter case there is an upper bound on $q$ which ... More
Simple foliated flowsJun 16 2019We describe transversely oriented foliations of codimension one on closed manifolds that admit simple foliated flows.
Twin and Pure Twin GroupJun 16 2019The twin group $T_n$ is a right angled Coxeter group generated by $n-1$ involutions and the pure twin group $PT_n$ is the kernel of the natural surjection from $T_n$ onto the symmetric group on $n$ symbols. In this paper, we investigate some structural ... More
Twin and pure twin groupsJun 16 2019Jun 22 2019The twin group $T_n$ is a right angled Coxeter group generated by $n-1$ involutions and the pure twin group $PT_n$ is the kernel of the natural surjection from $T_n$ onto the symmetric group on $n$ symbols. In this paper, we investigate some structural ... More
Learning in Cournot Games with Limited Information FeedbackJun 15 2019In this work, we study the interaction of strategic players in continuous action Cournot games with limited information feedback. Cournot game is the essential market model for many socio-economic systems where players learn and compete without the full ... More
Tangle decompositions of alternating link complementsJun 15 2019Decomposing knots and links into tangles is a useful technique for understanding their properties. The notion of prime tangles was introduced by Kirby and Lickorish in [2]; Lickorish proved [4] that by summing prime tangles one obtains a prime link. In ... More
L^2-Betti Numbers and Convergence of Normalized Hodge Numbers via the Weak Generic Nakano Vanishing TheoremJun 14 2019Jun 17 2019We study the rate of growth of normalized Hodge numbers along a tower of abelian covers of a smooth projective variety with semismall Albanese map. These bounds are in some cases optimal. Moreover, we compute the $L^2$-Betti numbers of irregular varieties ... More
L^2-Betti Numbers and Convergence of Normalized Hodge Numbers via the Weak Generic Nakano Vanishing TheoremJun 14 2019We study the rate of growth of normalized Hodge numbers along a tower of abelian covers of a smooth projective variety with semismall Albanese map. These bounds are in some cases optimal. Moreover, we compute the $L^2$-Betti numbers of irregular varieties ... More
On odd torsion in even Khovanov homologyJun 14 2019This short note resolves the most important part of the PS braid conjecture while introducing the first known examples of knots and links with odd torsion of order 9, 27, 81, and 25 in their even Khovanov homology.
FAQ on the g-theorem and the hard Lefschetz theorem for face ringsJun 14 2019This short review is the result of a minicourse at the Sapienza University of Rome the author gave about the proof of the $g$-theorem. We give a review over the two available proofs of the hard Lefschetz theorem for simplicial spheres, as well as recent ... More
FAQ on the g-theorem and the hard Lefschetz theorem for face ringsJun 14 2019Jun 26 2019This short review is the result of a minicourse at the Sapienza University of Rome the author gave about the proof of the $g$-theorem. We give a review over the two available proofs of the hard Lefschetz theorem for simplicial spheres, as well as recent ... More
FAQ on the g-theorem and the hard Lefschetz theorem for face ringsJun 14 2019Jun 24 2019This short review is the result of a minicourse at the Sapienza University of Rome the author gave about the proof of the $g$-theorem. We give a review over the two available proofs of the hard Lefschetz theorem for simplicial spheres, as well as recent ... More
2-systems of arcs on spheres with prescribed endpointsJun 14 2019Let $S$ be an $n$-punctured sphere, with $n \geq 3$. We prove that $\binom{n}{3}$ is the maximum size of a family of pairwise non-homotopic simple arcs on $S$ joining a fixed pair of distinct punctures of $S$ and pairwise intersecting at most twice. On ... More
Exhausting Curve Complexes by Finite Rigid Sets on Nonorientable SurfacesJun 13 2019Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components. Let $\mathcal{C}(N)$ be the curve complex of $N$. We prove that if $(g,n) = (3,0)$ or $g + n \geq 5$, then there is an exhaustion of $\mathcal{C}(N)$ by ... More
Perturbative analysis of the colored Alexander polynomial and KP soliton $τ$-functionsJun 13 2019In this paper we elaborate on the statement given in arXiv:1805.02761. Mainly, we study the relation between the colored Alexander polynomial and the famous KP hierarchy. We explain and prove this relation by exploring the fact that the dispersion equations ... More
Between buildings and free factor complexes: A Cohen-Macaulay complex for Out(RAAGs)Jun 13 2019For every finite graph $\Gamma$, we define a simplicial complex associated to the outer automorphism group of the RAAG $A_\Gamma$. These complexes are defined as coset complexes of parabolic subgroups of $Out^0(A_\Gamma)$ and interpolate between Tits ... More