2011 seminar talk: The character of topological groups, via Pontryagin-van Kampen duality and pcf theory
Talk held by Boaz Tsaban (Bar-Ilan University, Israel) at the KGRC seminar on 2011-09-14.
The Birkhoff-Kakutani Theorem asserts that a topological group is metrizable if and only if it has countable character. We develop and apply tools for the estimation of the character for a wide class of nonmetrizable topological groups. Even in the special case of free abelian topological groups, our results extend a number of results of Nickolas and Tkachenko, which were proved using laborious elementary methods.
Our method use a novel combination of (classical) descriptive set theory, Pontryagin-van Kampen duality, and pcf theory.
I will not assume knowledge of topological groups or any of the topics mentioned in the abstract or used in the talk. Students are, in particular, welcome.