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The Boundary Multiplicity of CAT(0) Groups

Frederick Ancel
University of Wisconsin at Milwaukee
Nov. 5, 2008, 12:15 p.m.
room 5850
Seminar Topology

Every hyperbolic (or negatively curved) group has a unique visual boundary. However, there are CAT(0) (or non-positively curved) groups that admit infinitely many non-homeomorphic boundaries. (The first example is due to C. Croke and B. Kleiner.) A previously unpublished proof (due to Ancel and J. Wilson) that this phenomenon occurs will be sketched. Other possible equivalence relations among the visual boundaries of a CAT(0) group will also be discussed; including equivariant homeomorphism and cell-like equivalence. The current state of knowledge about these relations will be described.