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Displaying 1 – 15 of 15

The abelianization of the Johnson kernel

Alexandru Dimca, Richard Hain, Stefan Papadima (2014)

Journal of the European Mathematical Society

We prove that the first complex homology of the Johnson subgroup of the Torelli group $T_{g}$ is a non-trivial, unipotent $T_{g}$ -module for all $g \geq 4$ and give an explicit presentation of it as a $S y m_{.} H_{1} (T_{g}, C)$ -module when $g \geq 6$ . We do this by proving that, for a finitely generated group $G$ satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the...

The asymptotic dimension of the first Grigorchuk group is infinity.

Justin Smith (2007)

Revista Matemática Complutense

We describe a sufficient condition for a finitely generated group to have infinite asymptotic dimension. As an application, we conclude that the first Grigorchuk group has infinite asymptotic dimension.

The Burau representation is not faithful for $n = 5$ .

Bigelow, Stephen (1999)

Geometry & Topology

The conjugacy problem for relatively hyperbolic groups.

Bumagin, Inna (2004)

Algebraic & Geometric Topology

The dual braid monoid

David Bessis (2003)

Annales scientifiques de l'École Normale Supérieure

The geometry of abstract groups and their splittings.

Charles Terence Clegg Wall (2003)

Revista Matemática Complutense

A survey of splitting theorems for abstract groups and their applications. Topics covered include preliminaries, early results, Bass-Serre theory, the structure of G-trees, Serre's applications to SL2 and length functions. Stallings' theorem, results about accessibility and bounds for splittability. Duality groups and pairs; results of Eckmann and collaborators on PD2 groups. Relative ends, the JSJ theorems and the splitting results of Kropholler and Roller on PDn groups. Notions of quasi-isometry,...

The isomorphism problem for toral relatively hyperbolic groups

François Dahmani, Daniel Groves (2008)

Publications Mathématiques de l'IHÉS

We provide a solution to the isomorphism problem for torsion-free relatively hyperbolic groups with abelian parabolics. As special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]). We also give a solution to the homeomorphism problem for finite volume hyperbolic $n$ -manifolds, for $n \geq 3$ . In the course of the proof of the main result,...

The Kazhdan property of the mapping class group of closed surfaces and the first cohomology group of its cofinite subgroups.

Taherkhani, Feraydoun (2000)

Experimental Mathematics

The mapping class group of a genus two surface is linear.

Bigelow, Stephen J., Budney, Ryan D. (2001)

Algebraic & Geometric Topology

The QSF property for groups and spaces.

Michael L. Mihalik, Stephen G. Brick (1995)

Mathematische Zeitschrift

The rank of actions on $R$ -trees

Damien Gaboriau, Gilbert Levitt (1995)

Annales scientifiques de l'École Normale Supérieure

The rhombic dodecahedron and semisimple actions of Aut(Fₙ) on CAT(0) spaces

Martin R. Bridson (2011)

Fundamenta Mathematicae

We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fₙ) has a fixed point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated ℤ⁴ ⊂ Aut(F₃) leaves invariant an isometrically embedded copy of Euclidean 3-space 𝔼³ ↪ X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet...

The symmetry of intersection numbers in group theory.

Scott, Peter (1998)

Geometry & Topology

The Tits alternative for $Out (F_{n})$ . I: Dynamics of exponentially-growing automorphisms.

Bestvina, Mladen, Feighn, Mark, Handel, Michael (2000)

Annals of Mathematics. Second Series

Trees of manifolds and boundaries of systolic groups

Paweł Zawiślak (2010)

Fundamenta Mathematicae

We prove that the Pontryagin sphere and the Pontryagin nonorientable surface occur as the Gromov boundary of a 7-systolic group acting geometrically on a 7-systolic normal pseudomanifold of dimension 3.

Currently displaying 1 – 15 of 15

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