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… Expand

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… Expand

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… Expand

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… Expand

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.Expand

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… Expand

We study the large scale geometry of mapping class groups MCG(S), using hyperbolicity properties of curve complexes. We show that any self quasi-isometry of MCG(S) (outside a few sporadic cases) is a… Expand

In [4] 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… Expand