Isomorphisms between big mapping class groups
Group Theory
2018-05-01 v3 Geometric Topology
Abstract
We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these `big' mapping class groups and shows that each finite-index subgroup has finite outer automorphism group. As a key ingredient, we prove that all simplicial automorphisms between curve complexes of infinite-type orientable surfaces are induced by homeomorphisms.
Cite
@article{arxiv.1708.08383,
title = {Isomorphisms between big mapping class groups},
author = {Juliette Bavard and Spencer Dowdall and Kasra Rafi},
journal= {arXiv preprint arXiv:1708.08383},
year = {2018}
}
Comments
v3: 11 pages; updated and added references; final version to appear in IMRN