Relatively hyperbolic Groups
- B. Bowditch
- MathematicsInternational journal of algebra and computation
- 6 May 2012
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.
Cut points and canonical splittings of hyperbolic groups
- B. Bowditch
- Mathematics
- 1 September 1998
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…
Tight geodesics in the curve complex
- B. Bowditch
- Mathematics
- 1 February 2008
The curve graph, $\mathcal{G}$, associated to a compact surface Σ is the 1-skeleton of the curve complex defined by Harvey. Masur and Minsky showed that this graph is hyperbolic and defined the…
Geometrical Finiteness for Hyperbolic Groups
- B. Bowditch
- Mathematics
- 1 May 1993
Abstract In this paper, we give an account of the notion of geometrical finiteness as applied to discrete groups acting on hyperbolic space of any dimension. We prove the equivalence of various…
Intersection numbers and the hyperbolicity of the curve complex
- B. Bowditch
- Mathematics
- 2006
Abstract We give another proof of the result of Masur and Minsky that the complex of curves associated to a compact orientable surface is hyperbolic. Our proof is more combinatorial in nature and can…
A topological characterisation of hyperbolic groups
- B. Bowditch
- Mathematics
- 1998
We characterise word hyperbolic groups as those groups which act properly discontinuously and cocompactly on the space of distinct triples of a compact metrisable space. This is, in turn, equivalent…
Natural triangulations associated to a surface
- B. Bowditch, D. Epstein
- Mathematics
- 1988
Coarse median spaces and groups
- B. Bowditch
- Mathematics
- 28 February 2013
We introduce the notion of a coarse median on a metric space. This satisfies the axioms of a median algebra up to bounded distance. The existence of such a median on a geodesic space is…
The Cannon–Thurston map for punctured-surface groups
- B. Bowditch
- Mathematics
- 26 July 2006
Let Γ be the fundamental group of a compact surface group with non-empty boundary. We suppose that Γ admits a properly discontinuous strictly type preserving action on hyperbolic 3-space such that…
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