Measure equivalence rigidity of the mapping class group

Research paper by Yoshikata Kida

Indexed on: 24 Jul '06Published on: 24 Jul '06Published in: Mathematics - Group Theory


We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme rigidity in the sense of measure equivalence: if the mapping class group is measure equivalent to a discrete group, then they are commensurable up to finite kernel. Moreover, we describe all lattice embeddings of the mapping class group into a locally compact second countable group. We also obtain similar results for finite direct products of mapping class groups.