English

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.

Keywords

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

R2 v1 2026-07-22T17:39:30.081Z