Kurt Gödel Research Center

2014 seminar talk: Complexity of Homeomorphism Relations up to Borel Reducibility

Talk held by Vadim Kulikov (KGRC) at the KGRC seminar on 2014-10-30.

Abstract

We will consider the program of determining the complexity of homeomorphism relations on various subclasses of Polish spaces such as compact, locally compact, sigma-compact, manifolds etc.. We will review the known classification and non-classification results and present some new ones. In particular we show that the homeomorphism on locally compact Polish spaces is classifiable by an equivalence relation induced by a Polish group action while the one on sigma-compact Polish spaces is not. In the end we will look at some open problems.