Resumen de Outer automorphism groups of equivalence relations for mapping class group actions

Yoshikata Kida

• We study outer automorphism groups Out() of equivalence relations 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() 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