Advanced Studies in Pure Mathematics

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

Yoshikata Kida

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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.

Article information

Source
Hyperbolic Geometry and Geometric Group Theory, K. Fujiwara, S. Kojima and K. Ohshika, eds. (Tokyo: Mathematical Society of Japan, 2017), 167-214

Dates
Received: 29 January 2015
Revised: 23 April 2015
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538671945

Digital Object Identifier
doi:10.2969/aspm/07310167

Mathematical Reviews number (MathSciNet)
MR3728498

Citation

Kida, Yoshikata. Splitting in orbit equivalence, treeable groups, and the Haagerup property. Hyperbolic Geometry and Geometric Group Theory, 167--214, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07310167. https://projecteuclid.org/euclid.aspm/1538671945


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