Adam Clay : The structure of the space of left-orderings

Posted by , part of the Logic Seminar.

At

Nov. 5, 2019, 3 p.m.

In

427 SEO

Abstract

A group G is called left-orderable if it admits a total ordering of its elements that is invariant under left multiplication. For a fixed group G, the set of all such orderings LO(G) can be topologized so as to become a compact space, in fact it is Polish whenever the group is countable and homeomorphic to a Cantor set whenever it admits no isolated points. This talk will be an introduction to LO(G), its topological properties and their connections to the algebra of the underlying group. I will also discuss a recent question of K. Mann concerning the structure of LO(G), and a strategy for tackling it in certain special cases.