Equivariant concentration in topological groups

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

We prove that, if G is a second-countable topological group with a compatible right-invariant metric d and (µn)nεℕ is a sequence of compactly supported Borel probability measures on G converging to invariance with respect to the mass transportation distance over d and such that (sptµn, d{up harpoon right}sptµnn{up harpoon right}sptµn)nεN concentrates to a fully supported, compact mm-space (X, dX,µX), then X is homeomorphic to a G-invariant subspace of the Samuel compactification of G. In particular, this confirms a conjecture by Pestov and generalizes a well-known result by Gromov and Milman on the extreme amenability of topological groups. Furthermore, we exhibit a connection between the average orbit diameter of a metrizable flow of an arbitrary amenable topological group and the limit of Gromov’s observable diameters along any net of Borel probability measures UEB-converging to invariance over the group.

Details

OriginalspracheEnglisch
Seiten (von - bis)925-956
Seitenumfang32
FachzeitschriftGeometry and Topology
Jahrgang23
Ausgabenummer2
PublikationsstatusVeröffentlicht - 2019
Peer-Review-StatusJa

Schlagworte

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