Universal properties of group actions on locally compact spaces

2013/12/20 by Hiroki Matui, Matui, Hiroki, Mikael Rørdam +1
Mathematics · #Advanced Topology and Set Theory #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1312.6027

Abstract

We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the β-compactification of G (which is a G-space in a natural way), and their minimal closed invariant subspaces. These are locally compact free G-spaces, and the latter are also minimal. We examine the properies of these G-spaces with emphasis on their universal properties. As an example of our resuts, we use combinatorial methods to show that each countable infinite group admits a free minimal action on the locally compact non-compact Cantor set.

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