Tohoku Mathematical Journal

Invariants of orbit equivalence relations and Baumslag-Solitar groups

Yoshikata Kida

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Abstract

To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class of the flow is shown to be an invariant of such actions of Baumslag-Solitar groups under weak orbit equivalence. Results on groups which are measure equivalent to Baumslag-Solitar groups are also provided.

Article information

Source
Tohoku Math. J. (2), Volume 66, Number 2 (2014), 205-258.

Dates
First available in Project Euclid: 9 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1404911861

Digital Object Identifier
doi:10.2748/tmj/1404911861

Mathematical Reviews number (MathSciNet)
MR3229595

Zentralblatt MATH identifier
1351.37016

Subjects
Primary: 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
Secondary: 20E06: Free products, free products with amalgamation, Higman-Neumann- Neumann extensions, and generalizations 20E08: Groups acting on trees [See also 20F65]

Keywords
Baumslag-Solitar groups orbit equivalence measure equivalence

Citation

Kida, Yoshikata. Invariants of orbit equivalence relations and Baumslag-Solitar groups. Tohoku Math. J. (2) 66 (2014), no. 2, 205--258. doi:10.2748/tmj/1404911861. https://projecteuclid.org/euclid.tmj/1404911861


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