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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
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 | ||||||||
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| 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: |
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| Date of first compliant deposit: | 9 August 2017 | ||||||||
| 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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