Cubulating Surface-by-free Groups
Let $$1 \to H \to G \to Q \to 1$$ be an exact sequence where $H= \pi_1(S)$ is the fundamental group of a closed surface $S$ of genus greater than one, $G$ is hyperbolic and $Q$ is finitely generated…
Cut points and canonical splittings of hyperbolic groups
In this paper, we give a construction of the JSJ splitting of a one-ended hyperbolic group (in the sense of Gromov [Gr]), using the local cut point structure of the boundary. In particular, this…
Atoroidal Surface Bundles Over Surfaces
A surface-by-surface group is an extension of a non-trivial orientable closed surface group by another such group. It is an open question as to whether every such group contains a free abelian…
Peripheral splittings of groups
We define the notion of a "peripheral splitting" of a group. This is essentially a representation of the group as the fundamental group of a bipartite graph of groups, where all the vertex groups…
Relatively hyperbolic Groups
- MathematicsInt. J. Algebra Comput.
This paper defines the boundary of a relatively hyperbolic group, and shows that the limit set of any geometrically finite action of the group is equivariantly homeomorphic to this boundary, and generalizes a result of Tukia for geometRically finite kleinian groups.
Deforming cubulations of hyperbolic groups
- MathematicsJournal of Topology
We describe a procedure to deform cubulations of hyperbolic groups by ‘bending hyperplanes’. Our construction is inspired by related constructions like Thurston's Mickey Mouse example, walls in…
SHOWING 1-9 OF 9 REFERENCES
Valuations and Finitely Presented Metabelian Groups
The equivariant Dehn's lemma and loop theorem
In  the authors observed that the topological methods in the theory of three-dimensional manifolds can be modified to settle some old problems in the classical theory of minimal surfaces in…
Groups, trees, and projective modules
Groups acting on graphs.- Fundamental groups.- Decompositions.- Cohomological dimension one.
Accessibility and Groups of Cohomological Dimension One