Tohoku Mathematical Journal
2014

June
SECOND SERIES VOL. 66, NO. 2

Tohoku Math. J.
66 (2014), 205-258

Title INVARIANTS OF ORBIT EQUIVALENCE RELATIONS AND BAUMSLAG-SOLITAR GROUPS

Author Yoshikata Kida

(Received September 3, 2012)
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.

Mathematics Subject Classification. Primary 37A20; Secondary 20E06, 20E08.

Key words and phrases. Baumslag-Solitar groups, orbit equivalence, measure equivalence.

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