Logic Seminar
Kostas Beros
University of Wisconsin-Madison
Universal Subgroups
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.
Tuesday November 6, 2012 at 4:00 PM in SEO 427