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Large-scale rigidity properties of the mapping class groups

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Bowditch, B. H. (2018) Large-scale rigidity properties of the mapping class groups. Pacific Journal of Mathematics, 293 (1). pp. 1-73. doi:10.2140/pjm.2018.293.1

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Official URL: http://doi.org/10.2140/pjm.2018.293.1

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Abstract

We study the coarse geometry of the mapping class group of a
compact orientable surface. We show that, apart from a few low-complexity cases, any quasi-isometric embedding of a mapping class group into itself agrees up to bounded distance with a left multiplication. In particular, such a map is a quasi-isometry. This is a strengthening of the result of Hamenst¨adt and of Behrstock, Kleiner, Minsky and Mosher that the mapping class groups are quasi-isometrically rigid. In the course of proving this, we also develop the
general theory of coarse median spaces and median metric spaces with a view to applications to Teichm¨uller space, and related spaces.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Teichmüller spaces, Group theory
Journal or Publication Title: Pacific Journal of Mathematics
Publisher: University of California, Berkeley
ISSN: 0030-8730
Official Date: 2018
Dates:
DateEvent
2018Published
3 November 2017Available
7 August 2017Accepted
Volume: 293
Number: 1
Page Range: pp. 1-73
DOI: 10.2140/pjm.2018.293.1
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
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