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Homological eigenvalues of mapping classes and torsion homology growth for fibered 3--manifolds
Homological eigenvalues mapping classes torsion homology growth fibered 3--manifolds Group Theory
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2012/5/9
Let S be an orientable surface with negative Euler characteristic, let \psi\in\Mod(S) be a mapping class of S, and let T_{\psi} be the mapping torus of \psi. We study the action of lifts of \psi on th...
Alexander varieties and largeness of finitely presented groups
Alexander varieties largeness of finitely presented groups Group Theory
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2012/5/9
Let X be a finite CW complex. We show that the fundamental group of X is large if and only if there is a finite cover Y of X and a sequence of finite abelian covers \{Y_N\} of Y which satisfy b_1(Y_N)...
A Note on Invariantly Finitely $L$-Presented Groups
Tietze transformations infinite presentations recursive presentations selfsimilar groups
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2012/5/9
In the first part of this note, we introduce Tietze transformations for $L$-presentations. These transformations enable us to generalize Tietze's theorem for finitely presented groups to invariantly f...
Detecting ends of residually finite groups in profinite completions
residually finite groups profinite completions Group Theory
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2012/5/24
Let $\C$ be a variety of finite groups. We use profinite Bass--Serre theory to show that if $u:H\hookrightarrow G$ is a map of finitely generated residually $\C$ groups such that the induced map $\hat...
Twisted split category algebras as quasi-hereditary algebras
Group Theory category algebras quasi-hereditary algebras
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2012/4/16
A category is called {\em split} if for every morphism $s\colon X\to Y$ there exists a morphism $t\colon Y\to X$ such that $s\circ t\circ s = s$. Let $C$ be a finite split category, let $k$ be a field...
On projective modules for Frobenius kernels and finite Chevalley groups
projective modules Frobenius kernels finite Chevalley groups Group Theory
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2012/4/23
Let $G$ be a simply-connected semisimple algebraic group scheme over an algebraically closed field of characteristic $p > 0$. Let $r \geq 1$ and set $q = p^r$. We show that if a rational $G$-module $M...
Lattices in hyperbolic buildings
Lattices hyperbolic buildings Group Theory
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2012/4/17
This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.
The space of bi-invariant orders on a nilpotent group
invariant order left-orderable group nilpotent group Group Theory
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2012/4/18
We prove a few basic facts about the space of bi-invariant (or left-invariant) total order relations on a torsion-free, nonabelian, nilpotent group G. For instance, we show that the space of bi-invari...
Notes on the Sigma-invariants - Part 1
Notes Sigma-invariants Group Theory
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2012/4/17
Memoir on the Sigma-invariants and their applications, Part 1.
Brauer's generalized decomposition numbers and universal deformation rings
Universal deformation rings Brauer’s generalized decomposition numbers tame blocks dihedral defect groups semidihedral defect groups
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2012/4/17
We study the problem of lifting to local rings certain mod 2 representations V of finite groups G which belong to 2-modular tame blocks B of G having at least two isomorphism classes of simple modules...
Amenable, transitive and faithful actions of groups acting on trees
Amenable transitive faithful actions groups trees
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2012/3/1
We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such...
Automorphisms of geometric structures associated to Coxeter groups
Automorphisms geometric structures associated Coxeter groups
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2012/3/1
In this paper, we consider the automorphism groups of the Cayley graph with respect to the Coxeter generators and the Davis complex of an arbitrary Coxeter group. We determine for which Coxeter groups...
A quasi-isometric embedding theorem for groups
quasi-isometric embedding theorem groups Group Theory
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2012/3/1
We show that every group $H$ of at most exponential growth with respect to some left invariant metric admits a bi-Lipschitz embedding into a finitely generated group $G$ such that $G$ is amenable (res...
A conjecture on B-groups
B-group Burnside ring biset functor
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2012/2/29
In this note, I propose the following conjecture: a finite group G is nilpotent if and only if its largest quotient B-group \beta(G) is nilpotent. I give a proof of this conjecture under the additiona...
The Metric Completion of Outer Space
The Metric Completion Outer Space the Lipschitz metric homeomorphic
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2012/3/1
We prove that the completion of Outer Space with the Lipschitz metric is homeomorphic to the free splitting complex. We give a new proof of a theorem by Francaviglia and Martino [FMa] that the isometr...