4 papers
Thick embeddings of graphs into symmetric spaces via coarse geometry
Benjamin Barrett, David Hume, Larry Guth +1
We prove estimates for the optimal volume of thick embeddings of finite graphs into symmetric spaces, generalising results of Kolmogorov-Barzdin and Gromov-Guth for embeddings into…
Local simple connectedness of boundaries of hyperbolic groups
Benjamin Barrett
In this paper we prove a theorem describing the local topology of the boundary of a hyperbolic group in terms of its global topology: the boundary is locally simply connected if an…
Computing the Cech cohomology of decomposition spaces
Benjamin Barrett
A line pattern in a free group is defined by a malnormal collection of cyclic subgroups. Otal defined a decomposition space associated to a line pattern. We provi…
Computing JSJ decompositions of hyperbolic groups
Benjamin Barrett
We present an algorithm that computes Bowditch's canonical JSJ decomposition of a given one-ended hyperbolic group over its virtually cyclic subgroups. The algorithm works by ident…