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 G_x 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 G_x 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 G_b=G and G_x 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