December 2:
Speaker: Ross Geoghegan (Binghamton)
Title: Cocompact proper CAT(0) spaces
This is joint work with Pedro Ontaneda. We prove that every
cocompact proper CAT(0) space is "almost geodesically complete" aka
"almost extendible" A basic ingredient of the proof of this
geometric statement is the topological theorem that there is a top
dimension d in which the compactly supported integral
cohomology of X is non-zero. We also prove that the
boundary-at-infinity (with cone topology) has Lebesgue covering
dimension d-1. In all this we do not assume that there is
any discrete cocompact group of isometries, not even a subgroup
having discrete orbits; however, a corollary for the discrete case
case is that ``the dimension of the boundary" is a quasi- isometry
invariant of CAT(0) groups. (By contrast, it is known that the
topological type of the boundary is not unique for a CAT(0) group.)