Alessandro Vignati: Homeomorphisms of Cech-Stone remainders

Place: Bahen Centre Information T (Room BA 2165)
Date: May 18, 2018 (13:30-15:00)
Speaker: Alessandro Vignati
Title: Homeomorphisms of Cech-Stone remainders
Abstract: From a locally compact space X one construct its Cech-Stone remainder X*=beta X minus X. We analyze the problem on whether X* and Y* can be homeomorphic for different spaces X and Y. In the 0-dimensional case, a solution to this problem has been proved to be independent of ZFC, by the work of Parovicenko, Farah, Dow-Hart and Farah-McKenney among others.
We prove, under PFA, the strongest possible rigidity result: for metrizable X and Y, we prove that X* is homeomorphic to Y* only if X and Y are homeomorphic modulo compact subsets. We also show that every homeomorphism X* –> Y* lifts to an homeomorphism between cocompact subsets of X and Y.

Leave a Reply

Your email address will not be published. Required fields are marked *

Time limit is exhausted. Please reload CAPTCHA.