Local simple connectedness of boundaries of hyperbolic groups

Abstract

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 and only if the complement of any point in the boundary is simply connected. This generalises a theorem of Bestvina and Mess.

22 pages. The second version clarifies the statement of theorem 1.2 and answers part of question 6.1