Atlas home || Conferences | Abstracts | about Atlas

Geometric Topology II
September 29 - October 5, 2002
Inter-University Center, Dubrovnik; Department of Mathematics, University of Zagreb
Dubrovnik, Croatia

Organizers
Ivan Ivansic, University of Zagreb;, James E. Keesling, University of Florida;, Alexander N. Dranishnikov, University of Florida;, Sime Ungar, University of Zagreb

View Abstracts
Conference Homepage

Equivariant compactifications of free G-spaces
by
Natella Antonyan
Universidad Nacional Autonoma de Mexico
Coauthors: Sergey Antonyan

Let G be a compact Lie group, X be a G-space and x be a point of X. The stabilizer Gx is defined to be the subgroup of all those elements g of G for which gx=x. A G-space X is called free whenever Gx is the trivial subgroup of G for every point x in X, and X is called based-free if there is a point b in X such that Gb=G and Gx is trivial for any x different from b. It is a well known result of R. Palais that each completely regular Hausdorff G-space can be embedded in a compact Hausdorff G-space.

In this talk we are going to present results that answer the following two questions:

(1) When a free G-space can be embedded in a compact based-free G-space?

(2) When a free G-space can be embedded in a compact free G-space?

Our results imply in combination with a result of A.N. Dranishnikov that if G is a finite group then for any n ³ 1 the n-dimensional Menger free G-compactum is a universal space for all separable, metrizable free G-spaces of dimension at most n.

Date received: August 30, 2002

Copyright © 2002 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 # caje-73.