Isomorphisms Between Big Mapping Class Groups-Reference-Cited by-同舟云学术

Isomorphisms Between Big Mapping Class Groups

Published:2018-05-25 Issue:10 Volume:2020 Page:3084-3099
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bavard Juliette¹,Dowdall Spencer²,Rafi Kasra³

Affiliation:

1. Univ Rennes, CNRS, IRMAR - UMR, Rennes, France

2. Department of Mathematics, Vanderbilt University, Nashville, USA

3. Department of Mathematics, University of Toronto, Toronto, Canada

Abstract

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.

Funder

National Science Foundation

Natural Sciences and Engineering Research Council of Canada

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2020/10/3084/33204892/rny093.pdf

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