Splitting in orbit equivalence, treeable groups, and the Haagerup property

Yoshikata Kida

Splitting in orbit equivalence, treeable groups, and the Haagerup property

Group Theory 2015-01-30 v2 Dynamical Systems Operator Algebras

Authors: Yoshikata Kida

Abstract

Let $G$ be a discrete countable group and $C$ its central subgroup with $G/C$ treeable. We show that for any treeable action of $G/C$ on a standard probability space $X$ , the groupoid $G\ltimes X$ is isomorphic to the direct product of $C$ and $(G/C)\ltimes X$ , through cohomology of groupoids. We apply this to show that any group in the minimal class of groups containing treeable groups and closed under taking direct products, commensurable groups and central extensions has the Haagerup property.

Keywords

treeable groups Haagerup property orbit equivalence groupoid cohomology central extension direct product commensurable groups

Cite

@article{arxiv.1403.0688,
  title  = {Splitting in orbit equivalence, treeable groups, and the Haagerup property},
  author = {Yoshikata Kida},
  journal= {arXiv preprint arXiv:1403.0688},
  year   = {2015}
}

Comments

31 pages, Theorem 1.4 improved

Splitting in orbit equivalence, treeable groups, and the Haagerup property

Abstract

Keywords

Cite

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