Christian Rosendal : Minimal metrics on topological groups

Posted by Kostyantyn Slutskyy , part of the Logic Seminar.

At

Feb. 24, 2015, 4 p.m.

In

SEO 427

Abstract

We discuss the problem of deciding when a metrisable topological group G has a canonically defined geometry in an identity neighbourhood. This naturally leads to the concept of minimal metrics on G, that we characterise in terms of a linear growth condition on powers of group elements. In turn, minimal metrics connect with Hilbert’s fifth problem for completely metrisable groups and we show, assuming that the set of squares is sufficiently rich, that every element of some identity neighbourhood belongs to a 1-parameter subgroup.