On the equivariant theory of covering spaces
by
Sylvia de Neymet
Universidad Nacional Autónoma de México
Coauthors: Rolando Jiménez

We define a G-covering space p : [X\tilde] --> X of a connected G-space X in such a way that p is a local G-homeomorphism. Suppose that p : [X\tilde] --> X is a G-covering space. If an additional condition is satisfied we say that p is a G-overlaying. Then p/G : [X\tilde]/G --> X/G is a covering space and p is a G-overlaying if and only if p/G is an overlaying. When G is compact, X is metric and p is a G-overlaying, then p has a G-overlaying extension q : [U\tilde] --> U, where X is a closed invariant subset of U. On the other hand we have that a local G-ANR is a G-ANR for metric spaces. So we obtain a G-ANR-resolution of [X\tilde] which covers a G-ANR-resolution of X and an equivariant lifting theorem for equivariant maps from arbitrary connected G-spaces (not necessarily locally connected).

Date received: March 17, 1997

Copyright © 1997 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 # caak-47.