Mathematics > Functional Analysis
[Submitted on 1 Jul 2023 (v1), last revised 1 May 2024 (this version, v2)]
Title:Amenability of finite energy path and loop groups
View PDF HTML (experimental)Abstract:It is shown that the groups of finite energy (that is, Sobolev class $H^1$) paths and loops with values in a compact Lie group are amenable in the sense of Pierre de la Harpe, that is, every continuous action of such a group on a compact space admits an invariant regular Borel probability measure. To our knowledge, the strongest previously known result concerned the amenability of groups of continuous paths and loops (Malliavin and Malliavin 1992).
Submission history
From: Vladimir Pestov [view email][v1] Sat, 1 Jul 2023 18:34:52 UTC (15 KB)
[v2] Wed, 1 May 2024 18:25:01 UTC (20 KB)
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