Alessandro Vignati: CH and homeomorphisms of Stone-Cech remainders

Place: Fields Institute (Room 210)

Date: June 3rd, 2016 (13:30-15:00)

Speaker: Alessandro Vignati

Title: CH and homeomorphisms of Stone-Cech remainders

Abstract:

If X is locally compact and Polish, it makes sense to ask how many homeomorphisms does X*, the Stone Cech remainder of X, have. It is known that, if X is 0-dimensional, under the Continuum Hypothesis X* has $2^{2^{\aleph_0}}$ many homeomorphisms (Rudin+Parovicenko). The same is true if $X=[0,1)$ (Yu, Dow-KP Hart), or if X is the disjoint union of countably many compact spaces (Coskey-Farah). But the question remains open for, for example, $X=\mathbb{R}^2$. We prove that for a large class of spaces (including $\mathbb{R}^n$, for all n) CH provides $2^{2^{\aleph_0}}$ many homeomorphisms of X*.