Geodesic
CAT(0) cube complexes and inner amenability
Bruno Duchesne1 ; Robin D. Tucker-Drob2 ; Phillip Wesolek3
1Université de Lorraine, Nancy, France
2Texas A&M University, College Station, USA
3Zendesk, USA
Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 371-411

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DOI

We here consider inner amenability from a geometric and group theoretical perspective. We prove that for every non-elementary action of a group G on a finite dimensional irreducible CAT(0) cube complex, there is a nonempty G-invariant closed convex subset such that every conjugation invariant mean on G gives full measure to the stabilizer of each point of this subset. Specializing our result to trees leads to a complete characterization of inner amenability for HNN-extensions and amalgamated free products. One novelty of the proof is that it makes use of the existence of certain idempotent conjugation-invariant means on G.
DOI : 10.4171/ggd/601
Classification : 20-XX, 43-XX
Mots-clés : CAT(0) cube complexes, inner amenability, wreath products, groups acting on trees

Bruno Duchesne  1   ; Robin D. Tucker-Drob  2   ; Phillip Wesolek  3

1 Université de Lorraine, Nancy, France
2 Texas A&M University, College Station, USA
3 Zendesk, USA 
Bruno Duchesne; Robin D. Tucker-Drob; Phillip Wesolek. CAT(0) cube complexes and inner amenability. Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 371-411. doi: 10.4171/ggd/601
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     pages = {371--411},
     year = {2021},
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     doi = {10.4171/ggd/601},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/601/}
}
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