Cantor Groups and the Free-Set Z-Set Conjecture
by
Robert Edwards
UCLA

A cantor group is a topological group which is homeomorphic to the cantor set (i.e., is an infinite profinite group, if you wish). Basic examples are 1) any countably infinite direct product of nontrivial finite groups, and 2) the p-adic integers, for your favorite prime p. The FSZS Conjecture is: Given any action by a cantor group on an ENR (= euclidean neighborhood retract), the free set of the action is a homology Z-set (in the ENR). This can be regarded as a sort of Super Hilbert-Smith Conjecture, the HSC being the case where the ENR is a manifold. This talk will discuss the (natural) classifying space approach to the FSZS Conjecture, and why I believe that I have cracked the free-action case.

Date received: March 3, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-56.