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Journal of the London Mathematical Society Advance Access published online on July 14, 2008
Journal of the London Mathematical Society, doi:10.1112/jlms/jdn042
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© 2008 London Mathematical Society

Outer automorphism groups of equivalence relations for mapping class group actions

Yoshikata Kida

Mathematical Institute
Tohoku University
Sendai 980-8578
Japan

We study outer automorphism groups Out(R) of equivalence relations R arising from ergodic, essentially free and measure-preserving actions on standard probability spaces of mapping class groups, and compute them explicitly for some examples. We show that the subgroups of Out(R) associated with action-automorphisms are always finite index ones. Moreover, a sharp upper bound of the indices among all such actions of mapping class groups is obtained.

2000 Mathematics Subject Classification 20F38, 37A20, 37A35.

Received August 9, 2007; revised April 30, 2008;
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