Dana Bartosova: Unique amenability of topological groups

Monday, November 4, 2013, 16.30
Seminar room 0.011, Mathematical Institute, University of Bonn

Speaker: Dana Bartosova (HIM Bonn)

Title: Unique amenability of topological groups

Abstract: A topological group is uniquely amenable if every ambit admits exactly one
invariant probability measure. An ambit is a dymanical system that contains a
dense orbit. A topological group is precompact if nitely many translates of every
open neighbourhood of the identity cover the whole group. Megrelishvilli, Pestov
and Uspenskij asked whether every uniquely amenable group is precompact. We
describe the universal ambit via near ultra lters and use this viewpoint to enlarge
the pool of groups for which the question has a positive question (e.g. groups of
automorphisms of structures or groups of isometries of homogeneous metric spaces
of regular density).

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