Universal properties of group actions on locally compact spaces.

Seminar by Mikael Rørdam

Abstract: The existence of universal minimal compact G-spaces, where G is a (discrete) group, is well-known. In this talk we show that one also has universal minimal G-spaces in the category of locally compact spaces. These universal spaces arise as minimal closed invariant subsets of open invariant subsets of the Stone-Cech compactification of the group G. We prove uniqueness and structure results for such spaces (under appropriate conditions). As a byproduct we show that each countable infinite group admits a free minimal action on the locally compact non-compact Cantor set.

This is a joint work with Hiroki Matui.