The Boundary Multiplicity of CAT(0) Groups
- Speaker(s)
- Frederick Ancel
- Affiliation
- University of Wisconsin at Milwaukee
- Date
- Nov. 5, 2008, 12:15 p.m.
- Room
- room 5850
- Seminar
- 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 A previously unpublished proof (due to Ancel and J.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.