Kostas Beros : Universal Subgroups

Posted by Lynn Scow , part of the Logic Seminar.

At

Nov. 6, 2012, 4 p.m.

In

SEO 427

Abstract

Given a topological group G and a family C of subgroups of G define a "universal C subgroup of G" to be a subgroup K in the family C such that every subgroup H in C is a continuous homomorphic pre-image of K. My recent work has shown that the countable power of a locally compact Polish group has universal compactly generated and K-sigma subgroups and that the countable power of an arbitrary Polish group has a universal analytic subgroup. For reasons I will explain in my talk, compactly generated, K-sigma and analytic subgroups are natural classes to work with in this context and share some useful properties. I will give some motivation for studying universal subgroups, summarize my results so far (including the ones above) and prove at least one of these results in the case of the Baer-Specker group.