Measure equivalence rigidity of the mapping class group
Group Theory
2015-02-02 v1 Geometric Topology
Abstract
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.
Cite
@article{arxiv.math/0607600,
title = {Measure equivalence rigidity of the mapping class group},
author = {Yoshikata Kida},
journal= {arXiv preprint arXiv:math/0607600},
year = {2015}
}
Comments
39 pages