Logic Seminar
Christian Rosendal
UIC
Minimal metrics on topological groups
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.
Tuesday February 24, 2015 at 4:00 PM in SEO 427