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Commensurability in Artin groups of spherical typeApr 20 2019Let $A$ and $A'$ be two Artin groups of spherical type, and let $A_1,\dots,A_p$ (resp. $A'_1,\dots,A'_q$) be the irreducible components of $A$ (resp. $A'$). We show that $A$ and $A'$ are commensurable if and only if $p=q$ and, up to permutation of the ... More

Handlebody Bundles and PolytopesApr 18 2019We construct examples of fibered three-manifolds with fibered faces all of whose monodromies extend to a handlebody.

Algebraic Structure of Diffeomorphism Groups of One-ManifoldsApr 18 2019It is a celebrated result of Mather that the group of $C^k$--diffeomorphisms of an $n$--manifold is simple, provided that a mild isotopy condition is satisfied, with the possible exception of $k=n+1$. The purpose of this article is mostly expository, ... More

Axially-Symmetric Exact Solutions for Majorana Fermions with GravityApr 18 2019In this paper, we consider Majorana spinor fields in interaction with their own gravitational field: for this case we present axially-symmetry exact solutions. Final comments are given.

Conjugacy of Levi subgroups of reductive groups and a generalization to linear algebraic groupsApr 18 2019We investigate Levi subgroups of a connected reductive algebraic group G, over a ground field K. We parametrize their conjugacy classes in terms of sets of simple roots and we prove that two Levi K-subgroups of G are rationally conjugate if and only if ... More

Scl in graphs of groupsApr 17 2019Let G be a group acting on a tree with cyclic edge and vertex stabilizers. Then stable commutator length (scl) is rational in G. Furthermore, scl varies predictably and converges to rational limits in so-called "surgery" families. This is a homological ... More

The power word problemApr 17 2019In this work we introduce a new succinct variant of the word problem in a finitely generated group $G$, which we call the power word problem: the input word may contain powers $p^x$, where $p$ is a finite word over generators of $G$ and $x$ is a binary ... More

Mapping class group is generated by four involutionsApr 17 2019We prove that the mapping class group of a closed connected orientable surface of genus at least three is generated by four involutions.

Character Levels and Character Bounds. IIApr 17 2019This paper is a continuation of [GLT], which develops a level theory and establishes strong character bounds for finite simple groups of linear and unitary type in the case that the centralizer of the element has small order compared to $|G|$ in a logarithmic ... More

Character Levels and Character Bounds. IIApr 17 2019Apr 19 2019This paper is a continuation of [GLT], which develops a level theory and establishes strong character bounds for finite simple groups of linear and unitary type in the case that the centralizer of the element has small order compared to $|G|$ in a logarithmic ... More

Fuchs' problem for 2-groupsApr 16 2019Nearly $60$ years ago, L\'{a}szl\'{o} Fuchs posed the problem of determining which groups can be realized as the group of units of a commutative ring. To date, the question remains open, although significant progress has been made. Along this line, one ... More

Tits Alternative for groups acting properly on $2$-dimensional recurrent complexesApr 16 2019We prove the Tits Alternative for groups with a bound on the order of finite subgroups, acting properly on $2$-dimensional "recurrent" complexes. This class of complexes includes, among others: $2$-dimensional buildings, $2$-dimensional systolic complexes, ... More

A short proof of Thoma's theorem on type I groupsApr 16 2019In the theory of unitary group representations, a group is called type I if all factor representations are of type I, and by a celebrated theorem of James Glimm [Gli61b], the type I groups are precisely those groups for which the irreducible unitary representations ... More

Free Proalgebraic GroupsApr 16 2019Replacing finite groups by linear algebraic groups, we study an algebraic-geometric counterpart of the theory of free profinite groups. In particular, we introduce free proalgebraic groups and characterize them in terms of embedding problems. The main ... More

Intersections of subgroups in virtually free groups and virtually free productsApr 15 2019This note contains a (short) proof of the following generalisation of the Friedman--Mineyev theorem (earlier known as the Hanna Neumann conjecture): if $A$ and $B$ are nontrivial free subgroups of a virtually free group containing a free subgroup of index ... More

Intersections of subgroups in virtually free groups and virtually free productsApr 15 2019Apr 17 2019This note contains a (short) proof of the following generalisation of the Friedman--Mineyev theorem (earlier known as the Hanna Neumann conjecture): if $A$ and $B$ are nontrivial free subgroups of a virtually free group containing a free subgroup of index ... More

Globalization of group cohomology in the sense of Alvares-Alves-RedondoApr 15 2019Apr 17 2019Recently E. R. Alvares, M. M. Alves and M. J. Redondo introduced a cohomology for a group $G$ with values in a module over the partial group algebra $K_{\mathrm{par}}(G)$, which is different from the partial group cohomology defined earlier by the first ... More

Globalization of group cohomology in the sense of Alvares-Alves-RedondoApr 15 2019Recently E. R. Alvares, M. M. Alves and M. J. Redondo introduced a cohomology for a group $G$ with values in a module over the partial group algebra $K_{\mathrm{par}}(G)$, which is different from the partial group cohomology defined earlier by the first ... More

Examples of Connective C*-algebrasApr 15 2019We prove that any torsion free crystallographic group with the infinite abelianization is connective.

Finite groups with $\mathfrak{F}$-subnormal normalizers of Sylow subgroupsApr 15 2019Let $\pi$ be a set of primes and $\mathfrak{F}$ be a formation. In this article a properties of the class ${\rm w}^{*}_{\pi}\mathfrak{F}$ of all groups $G$, such that $\pi(G)\subseteq \pi(\mathfrak{F})$ and the normalizers of all Sylow $p$-subgroups of ... More

A generally covariant measurement scheme for quantum field theory in curved spacetimesApr 15 2019We propose and develop a measurement scheme for quantum field theory (QFT) in curved spacetimes, in which the QFT of interest, the "system", is dynamically coupled to another, the "probe", in a compact spacetime region. Measurements of observables in ... More

Sullivan's structural stability of expanding group actionsApr 15 2019In his 1985 paper Sullivan sketched a proof of his structural stability theorem for group actions satisfying certain expansion-hyperbolicity axioms. We generalize the theorem by weakening these axioms substantially, while adding more details to Sullivan's ... More

Symmetry breaking and lattice kirigami: finite temperature effectsApr 15 2019Recent work has analysed how deformations due to the insertion of a defect in a flat hexagonal lattice affect the ground state structure of an interacting fermion field theory. Such modifications result in an increase of the order parameter in the vicinity ... More

Virtual Specialness of certain graphs of special cube complexesApr 15 2019We investigate the virtual specialness of a compact cube complex $X$ that splits as a graph of nonpositively curved cube complexes. We prove virtual specialness of $X$ when each vertex space of $X$ has word-hyperbolic $\pi_1$ and $\pi_1X$ has ``finite ... More

The automorphism groups of the profinite braid groupsApr 14 2019In this paper we determine the automorphism groups of the profinite braid groups with four or more strings in terms of the profinite Grothendieck-Teichm\"uller group.

On a lattice characterization of finite soluble $PST$-groupsApr 14 2019Let $\mathfrak{F}$ be a class of finite groups and $G$ a finite group. Let ${\cal L}_{\mathfrak{F}}(G)$ be the set of all subgroups $A$ of $G$ with $A^{G}/A_{G}\in \mathfrak{F}$. A chief factor $H/K$ of $G$ is $\mathfrak{F}$-central in $G$ if $(H/K)\rtimes ... More

On topological complexity of hyperbolic groupsApr 14 2019We show that the topological complexity of a finitely generated torsion free hyperbolic group $\pi$ with $\cd\pi=n$ equals $2n$.

The semigroup of monotone co-finite partial homeomorphisms of the real lineApr 14 2019In the paper we investigate the semigroup of monotone co-finite partial homeomorphisms of the space of the usual real line $\mathbb{R}$. We prove that the inverse semigroup $\mathscr{P\!\!H}^+_{\!\!\operatorname{\textsf{cf}}}\!(\mathbb{R})$ is factorizable ... More

On the semigroup $\textbf{ID}_{\infty}$Apr 14 2019We study the semigroup $\textbf{{ID}}_{\infty}$ of all partial isometries of the set of integers $\mathbb{Z}$. It is proved that the quotient semigroup $\textbf{{ID}}_{\infty}/\mathfrak{C}_{\textsf{mg}}$, where $\mathfrak{C}_{\textsf{mg}}$ is the minimum ... More

The number of fuzzy subgroups of a finite abelian group of order $p^{n}q^{m}$Apr 14 2019The purpose of this paper is to determine the number of fuzzy subgroups of a finite abelian group of order $p^{n}q^{m}$. As an application of our main result, explicit formulas for the number of fuzzy subgroups of $\mathbb{Z}_{p}^{n}\times\mathbb{Z}_{q}^{m}$ ... More

The semigroup of partial co-finite isometries of positive integersApr 14 2019The semigroup $\mathbf{I}\mathbb{N}_{\infty}$ of all partial co-finite isometries of positive integers is studied. We describe Green's relations on the semigroup $\mathbf{I}\mathbb{N}_{\infty}$, its band and proved that $\mathbf{I}\mathbb{N}_{\infty}$ ... More

Lucas sequences in $t$-uniform simplicial complexesApr 13 2019We introduce $t$-uniform simplicial complexes and we show that the lengths of spheres in such complexes are the terms of certain Lucas sequences. We find optimal constants for the linear isoperimetric inequality in the hyperbolic case.

Groups with few $p'$-character degreesApr 13 2019We prove a variation of Thompson's Theorem. Namely, if the first column of the character table of a finite group $G$ contains only two distinct values not divisible by a given prime number $p>3$, then $O^{pp'pp'}(G)=1$. This is done by using the classification ... More

A rotation group whose subspace arrangement is not from a real reflection groupApr 12 2019Apr 18 2019We exhibit a family of real rotation groups whose subspace arrangements are not contained in that of any real reflection group, answering a question of Martino and Singh.

A rotation group whose subspace arrangement is not from a reflection groupApr 12 2019We exhibit a family of real rotation groups whose subspace arrangements are not contained in that of any real reflection group, answering a question of Martino and Singh.

Minimal energy cost of entanglement extractionApr 12 2019We compute the minimal energy cost for extracting entanglement from the ground state of a bosonic or fermionic quadratic system. Specifically, we find the minimal energy increase in the system resulting from replacing an entangled pair of modes, sharing ... More

MAT-free reflection arrangementsApr 12 2019We introduce the class of MAT-free hyperplane arrangements which is based on the Multiple Addition Theorem by Abe, Barakat, Cuntz, Hoge, and Terao. We also investigate the closely related class of MAT2-free arrangements based on a recent generalization ... More

Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl TensorApr 12 2019We derive a superpotential for null electromagnetic fields in which the field line structure is in the form of an arbitrary torus knot. These fields are shown to correspond to single copies of a class of anti-self-dual Kerr-Schild spacetimes containing ... More

Stature and separability in graphs of groupsApr 12 2019We introduce the notion of finite stature of a family $\{H_i\}$ of subgroups of a group $G$. We investigate the separability of subgroups of a group $G$ that splits as a graph of hyperbolic special groups with quasiconvex edge groups. We prove that when ... More

On $p$-compact group topologies on direct sums of ${\mathbb Q}$Apr 11 2019We prove that if $p$ is a selective ultrafilter then ${\mathbb Q}^{(\kappa)}$ has a $p$-compact group topology without non-trivial convergent sequences, for each infinite cardinal $\kappa =\kappa^\omega$. In particular, this gives the first arbitrarily ... More

A survey on extensions of Riemannian manifolds and Bartnik mass estimatesApr 11 2019Mantoulidis and Schoen developed a novel technique to handcraft asymptotically flat extensions of Riemannian manifolds $(\Sigma \cong \mathbb{S}^2,g)$, with $g$ satisfying $\lambda_1 = \lambda_1(-\Delta_g + K(g))>0$, where $\lambda_1$ is the first eigenvalue ... More

A new characterization of the Haagerup propertyApr 11 2019Apr 16 2019The aim of the article is to provide a characterization of the Haagerup property for locally compact, second countable groups in terms of actions on $\sigma$-finite measure spaces.

A new characterization of the Haagerup propertyApr 11 2019The aim of the article is to provide a characterization of the Haagerup property for locally compact, second countable groups in terms of actions on $\sigma$-finite measure spaces.

The set of numerical semigroups of a given multiplicity and Frobenius numberApr 11 2019We study the structure of the family of numerical semigroups with fixed multiplicity and Frobenius number. We give an algorithmic method to compute all the semigroups in this family. As an application we compute the set of all numerical semigroups with ... More

Comparing the Roller and B(X) boundaries of CAT(0) cube complexesApr 10 2019The Roller boundary is a well-known compactification of a CAT(0) cube complex X. When X is locally finite, essential, irreducible, non-Euclidean and admits a cocompact action by a group G, Nevo-Sageev show that a subset, B(X), of the Roller boundary is ... More

Homogeneous length functions on Groups: Intertwined computer & human proofsApr 10 2019We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human readable proof was ... More

On the automorphism group of the universal homogeneous meet-treeApr 10 2019We show that the countable universal homogeneous meet-tree has a generic automorphism, but it does not have a generic pair of automorphisms.

On the automorphism group of the universal homogeneous meet-treeApr 10 2019Apr 16 2019We show that the countable universal homogeneous meet-tree has a generic automorphism, but it does not have a generic pair of automorphisms.

The lattice Burnside ringsApr 10 2019We introduce the concept of lattice Burnside ring for a finite group G associated to a family of nonempty sublattices of a finite G-lattice assigned to subgroups of G. The slice Burnside ring introduced by S. Bouc is isomorphic to a lattice Burnside ring. ... More

High Performance Reconfigurable Computing SystemsApr 10 2019The rapid progress and advancement in electronic chips technology provide a variety of new implementation options for system engineers. The choice varies between the flexible programs running on a general-purpose processor (GPP) and the fixed hardware ... More

The linear stability of Reissner-Nordström spacetime for small chargeApr 09 2019In this thesis, we prove the linear stability to gravitational and electromagnetic perturbations of the Reissner-Nordstr\"om family of charged black holes with small charge. Solutions to the linearized Einstein-Maxwell equations around a Reissner-Nordstr\"om ... More

Borel's stable range for the cohomology of arithmetic groupsApr 09 2019In this note, we remark on the range in Borel's theorem on the stable cohomology of the arithmetic groups Sp(2n,Z) and SO(n,n;Z). This improves the range stated in Borel's original papers, an improvement that was known to Borel. Our main task is a technical ... More

Complete graph decompositions and p-groupoidsApr 09 2019We study P-groupoids that arise from certain decompositions of complete graphs. We show that left distributive P-groupoids are distributive, quasigroups. We characterize P-groupoids when the corresponding decomposition is a Hamiltonian decomposition for ... More

Coarse geometry of the fire retaining property and group splittingsApr 09 2019Given a non-decreasing function $f \colon \mathbb{N} \to \mathbb{N}$ we define a single player game on (infinite) connected graphs that we call fire retaining. If a graph $G$ admits a winning strategy for any initial configuration (initial fire) then ... More

Poorly connected groupsApr 09 2019We investigate groups whose Cayley graphs have poorly connected subgraphs. We prove that a finitely generated group admits a Lipschitz bounded-to-one map to a bounded degree tree if and only if it is virtually free. We then prove a gap theorem for connectivity ... More

Virtually cyclic dimension for 3-manifold groupsApr 09 2019Let G be the fundamental group of a connected, closed, orientable 3-manifold. We explicitly compute its virtually cyclic geometric dimension. Among the tools we use are the prime and JSJ decompositions of M, several push-out type constructions, as well ... More

Floer homology, group orderability, and taut foliations of hyperbolic 3-manifoldsApr 09 2019This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and admitting a co-orientable taut foliation. In particular, it ... More

Developable surface patches bounded by NURBS curvesApr 09 2019In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary curves. The ... More

Bogomolov multiplier and the Lazard correspondenceApr 09 2019In this paper we extend the notion of CP covers for groups to the field of Lie algebras, and show that despite the case of groups, all CP covers of a Lie algebra are isomorphic. Finally we show that CP covers of groups and Lie rings which are in Lazard ... More

Some questions for possible submission to the next Kourovka notebookApr 08 2019This is a collection of questions that I am considering submitting to the next edition of the Kourovka Notebook of open questions in group theory. Most are questions I raised in papers between 1981 and the present; a few are new. I welcome feedback.

Computation of Hopf Galois structures on separable extensions and classification of those for degree twice an odd prime powerApr 08 2019A Hopf Galois structure on a finite field extension $L/K$ is a pair $(H,\mu)$, where $H$ is a finite cocommutative $K$-Hopf algebra and $\mu$ a Hopf action. In this paper we present a program written in the computational algebra system Magma which gives ... More

Permutations with a distinct divisor propertyApr 08 2019A finite group of order $n$ is said to have the distinct divisor property (DDP) if there exists a permutation $g_1,\ldots, g_n$ of its elements such that $g_i^{-1}g_{i+1} \neq g_j^{-1}g_{j+1}$ for all $1\leq i<j<n$. We show that an abelian group is DDP ... More

From independent sets and vertex colorings to isotropic spaces and isotropic decompositionsApr 08 2019In the 1970's, Lov\'asz built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings (FCT 1979). A similar connection between bipartite graphs and matrix spaces plays a key role in the recent resolutions of the non-commutative ... More

Cohomological induction and uniform measure equivalenceApr 08 2019We construct a general cohomological induction isomorphism from a uniform measure equivalence of locally compact, second countable, unimodular groups which, as a special case, yields that the graded cohomology rings of quasi-isometric, connected, simply ... More

On the Wilson Monoid of a Pairwise Balanced DesignApr 08 2019We give a new perspective of the relationship between simple matroids of rank 3 and pairwise balanced designs, connecting Wilson's theorems and tools with the theory of truncated boolean representable simplicial complexes. We also introduce the concept ... More

On one question of Shemetkov about composition formationsApr 07 2019In this paper one construction of composition formations was introduced. This construction contains formations of quasinilpotent groups, $c$-supersoluble groups, groups defined by ranks of chief factors and some new classes of groups. A partial answer ... More

Elementary proof of symmetry of the off-diagonal Seeley-DeWitt (and related Hadamard) coefficientsApr 07 2019We will prove in an elementary way that off-diagonal Seeley-DeWitt and Hadamard coefficients are (sesqui-)symmetric for smooth manifolds of arbitrary signature.

Non self-adjointness of the Klein-Gordon operator on globally hyperbolic and geodesically complete manifold. An exampleApr 07 2019We describe a Lorentzian manifold that is globally hyperbolic and geodesically complete, but such that the (minimally coupled) Klein-Gordon operator with the standard domain is not essentially self-adjoint.

Supersymmetric near-horizon geometry and Einstein-Cartan-Weyl spacesApr 07 2019We show that the horizon geometry for supersymmetric black hole solutions of minimal five-dimensional gauged supergravity is that of a particular Einstein-Cartan-Weyl (ECW) structure in three dimensions, involving the trace and traceless part of both ... More

Conjugating automorphisms of graph products: Kazhdan's property (T) and SQ-universalityApr 07 2019An automorphism of a graph product of groups is conjugating if it sends each factor to a conjugate of a factor (possibly different). In this article, we determine precisely when the group of conjugating automorphisms of a graph product satisfies Kazhdan's ... More

The average character degree and an improvement of the Ito-Michler theoremApr 07 2019The classical It\^{o}-Michler theorem states that the degree of every ordinary irreducible character of a finite group $G$ is coprime to a prime $p$ if and only if the Sylow $p$-subgroups of $G$ are abelian and normal. In an earlier paper, we used the ... More

Harmonic Models and BernoullicityApr 06 2019We give many examples of algebraic actions which are factors of Bernoulli shifts. These include certain harmonic models over left orderable groups of large enough growth, as well as algebraic actions associated to certain lopsided elements in any left ... More

Detecting structural properties of finite groups by the sum of element ordersApr 06 2019In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.

Manifold-based isogeometric analysis basis functions with prescribed sharp featuresApr 05 2019We introduce manifold-based basis functions for isogeometric analysis of surfaces with arbitrary smoothness, prescribed $C^0$ continuous creases and boundaries. The utility of the manifold-based surface construction techniques in isogeometric analysis ... More

Almost symmetric numerical semigroups with high typeApr 05 2019We establish a one-to-one correspondence between numerical semigroups of genus $g$ and almost symmetric numerical semigroups with Frobenius number $F$ and type $F-2g$, provided that $F$ is greater than $4g-1$.

Contracting asymptotics of the lapse-scalar field sub-system of the Einstein-scalar field equationsApr 05 2019We prove an asymptotic stability result for a linear coupled hyperbolic-elliptic system on a large class of singular background spacetimes in CMC gauge on the n-torus. At each spatial point these background spacetimes are perturbations of Kasner-like ... More

Asymptotics with a positive cosmological constant: IV. The `no-incoming radiation' conditionApr 04 2019Consider compact objects --such as neutron star or black hole binaries-- in \emph{full, non-linear} general relativity. In the case with zero cosmological constant $\Lambda$, the gravitational radiation emitted by such systems is described by the well ... More

On the number of non-G-equivalent minimal abelian codesApr 04 2019Let $G$ be a finite abelian group. We prove that the number of non-$G$-equivalent minimal abelian codes is equal to number of divisors of the exponent of $G$ if and only if for each prime $p$ dividing the order of $G$, the Sylow $p$-subgroups of $G$ are ... More

Amenability and computabilityApr 04 2019In this paper we extend the approach of M. Cavaleri to effective amenability to the class of computably enumerable groups, i.e. in particular we do not assume that groups are finitely generated. In the case of computable groups we also study complexity ... More

Uniform Kazhdan Constants and Paradoxes of the Affine PlaneApr 04 2019Let $G=\mathrm{SL}(2,\mathbb{Z})\ltimes\mathbb{Z}^2$ and $H=\mathrm{SL}(2,\mathbb{Z})$. We prove that the action $G\curvearrowright\mathbb{R}^2$ is uniformly non-amenable and that the quasi-regular representation of $G$ on $\ell^2(G/H)$ has a uniform ... More

Perturbations of the Lambda-CDM model in a dynamical systems perspectiveApr 04 2019The observational success and simplicity of the $\Lambda$CDM model, and the explicit analytic perturbations thereof, set the standard for any alternative cosmology. It therefore serves as a comparison ground and as a test case for methods which can be ... More

Words, permutations, and the nonsolvable length of a finite groupApr 04 2019We study the impact of certain identities and probabilistic identities on the structure of finite groups. More specifically, let $w$ be a nontrivial word in $d$ distinct variables and let $G$ be a finite group for which the word map $w_G:G^d\rightarrow ... More

The Hanna Neumann conjecture for Demushkin GroupsApr 03 2019We confirm the Hanna Neumann conjecture for topologically finitely generated closed subgroups $U$ and $W$ of a nonsolvable Demushkin group $G$. Namely, we show that \begin{equation*} \sum_{g \in U \backslash G/W} \bar d(U \cap gWg^{-1}) \leq \bar d(U) ... More

Hyperbolic structures for Artin-Tits groups of spherical typeApr 03 2019The goal of this mostly expository paper is to present several candidates for hyperbolic structures on irreducible Artin-Tits groups of spherical type and to elucidate some relations between them. Most constructions are algebraic analogues of previously ... More

Ozawa's class $\mathcal S$ for locally compact groups and unique prime factorizationApr 03 2019We study class $\mathcal S$ for locally compact groups. We characterize locally compact groups in this class as groups having an amenable action on a boundary that is small at infinity, generalizing a theorem of Ozawa. Using this characterization, we ... More

Topological restrictions on Anosov representationsApr 03 2019We characterize groups admitting Anosov representations into $\mathsf{SL}(3,\mathbb R)$, projective Anosov representations into $\mathsf{SL}(4,\mathbb R)$, and Borel Anosov representations into $\mathsf{SL}(4,\mathbb R)$. More generally, we obtain bounds ... More

Global local coversApr 02 2019This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.

An effective Lie--Kolchin theorem for quasi-unipotent matricesApr 01 2019Apr 05 2019We establish an effective version of the classical Lie--Kolchin Theorem. Namely, let $A,B\in\mathrm{GL}_m(\mathbb{C})$ be quasi--unipotent matrices such that the Jordan Canonical Form of $B$ consists of a single block, and suppose that for all $k\geq0$ ... More

An effective Lie--Kolchin theorem fro quasi-unipotent matricesApr 01 2019We establish an effective version of the classical Lie--Kolchin Theorem. Namely, let $A,B\in\mathrm{GL}_m(\mathbb{C})$ be quasi--unipotent matrices such that the Jordan Canonical Form of $B$ consists of a single block, and suppose that for all $k\geq0$ ... More

The geometry of small causal diamonds in vacuumApr 01 2019The geometry of small causal diamonds in the absence of matter is considered, based on three distinct constructions that are common in the literature, namely the geodesic ball, Alexandrov interval and lightcone cut. The causal diamond geometry is studied ... More

On a generalization of the Howe-Moore propertyApr 01 2019We define a Howe-Moore property relative to a set of subgroups. Namely, a group $G$ has the Howe-Moore property relative to a set $\mathcal{F}$ of subgroups if for every unitary representation $\pi$ of $G$, whenever the restriction of $\pi$ to any element ... More

Algebraic, combinatorial and topological properties of singular virtual braid monoidsApr 01 2019Apr 02 2019In this paper we discuss algebraic, combinatorial and topological properties of singular virtual braids. On the algebraic side we state the relations between classical and virtual singular objects, in addition we discuss a Birman-like conjecture for the ... More

Geometry and topology of the Kerr photon region in the phase spaceApr 01 2019We study the set of trapped photons of a subcritical (a<M) Kerr spacetime as a subset of the phase space. First, we present an explicit proof that the photons of constant Boyer--Lindquist coordinate radius are the only photons in the Kerr exterior region ... More

Characteristic varieties of graph manifolds and quasi-projectivity of fundamental groups of algebraic linksApr 01 2019The present paper studies the structure of characteristic varieties of fundamental groups of graph manifolds. As a consequence, a simple proof of Papadima's question is provided on the characterization of algebraic links that have quasi-projective fundamental ... More

1-smooth pro-p groups and the Bloch-Kato conjectureApr 01 2019Let $p$ be a prime. We study pro-$p$ groups $G$ endowed with a continuous homomorphism $G\to1+p\mathbb{Z}_p$ satisfying a formal version of Hilbert 90. These pro-$p$ groups are particularly important in Galois theory because by Kummer theory maximal pro-$p$ ... More

1-smooth pro-p groups and the Bloch-Kato conjectureApr 01 2019Apr 04 2019Let $p$ be a prime. We study pro-$p$ groups $G$ endowed with a continuous homomorphism $G\to1+p\mathbb{Z}_p$ satisfying a formal version of Hilbert 90. These pro-$p$ groups are particularly important in Galois theory because by Kummer theory maximal pro-$p$ ... More

On the characters of Sylow $p$-subgroups of finite Chevalley groups $G(p^f)$ for arbitrary primesApr 01 2019We develop in this work a method to parametrize the set $\mathrm{Irr}(U)$ of irreducible characters of a Sylow $p$-subgroup $U$ of a finite Chevalley group $G(p^f)$ which is valid for arbitrary primes $p$, in particular when $p$ is a very bad prime for ... More

A Poisson transform adapted to the Rumin complexApr 01 2019Let $G$ be a semisimple Lie group with finite center, $K\subset G$ a maximal compact subgroup, and $P\subset G$ a parabolic subgroup. Following ideas of P.Y.\ Gaillard, one may use $G$-invariant differential forms on $G/K\times G/P$ to construct $G$-equivariant ... More

The Möbius function of ${\rm PSL}(3,2^p)$ for any prime $p$Mar 31 2019Let $G$ be the simple group ${\rm PSL}(3,2^p)$, where $p$ is a prime number. For any subgroup $H$ of $G$, we compute the M\"obius function of $H$ in the subgroup lattice of $G$. To this aim, we describe the intersections of maximal subgroups of $G$. We ... More