Sam Ziegler & Phil Wesolek : Weak Equivalence / Conjugacy classes in locally compact subgroups of S_{\infty}

Posted by Sam Ziegler , part of the Louise Hay Logic Seminar.

At

Sept. 19, 2013, 4 p.m.

In

SEO 427

Abstract

Sam will speak about the relation of weak equivalence between actions of discrete groups on the interval [0,1], in particular the non-classifiability of this relation. Phil will speak about the following: many closed subgroups of S_{\infty} admit a comeagre conjugacy class. For example, S_{\infty} (folklore) or Aut(\mathbb{Q},<) (Truss) admit a comeagre conjugacy class. Kechris and Rosendal ask if a locally compact subgroup of S_{\infty} can admit a comeagre conjugacy class. We answer the question in the negative via an analysis of locally compact subgroups of S_{\infty} with topological conditions on a conjugacy class.