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Large-scale rank and rigidity of the Weil-Petersson metric
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Bowditch, B. H. (2020) Large-scale rank and rigidity of the Weil-Petersson metric. Groups, Geometry and Dynamics, 14 (2). pp. 607-652. doi:10.4171/GGD/557 ISSN 1661-7207.
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Official URL: https://doi.org/ 10.4171/GGD/557
Abstract
We study the large-scale geometry of Weil–Petersson space, that is, Teichmüller space equipped with theWeil–Petersson metric. We show that this admits a natural coarse median structure of a specific rank. Given that this is equal to the maximal dimension of a quasi-isometrically embedded euclidean space,we recover a result of Eskin,Masur and Rafi which gives the coarse rank of the space. We go on to show that, apart from finitely many cases, the Weil–Petersson spaces are quasi-isometrically distinct, and quasi-isometrically rigid. In particular, any quasi-isometry between such spaces is a bounded distance from an isometry. By a theorem of Brock,Weil–Petersson space is equivariantly quasi-isometric to the pants graph, so our results apply equally well to that space.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Weil conjectures , Geometry, Algebraic , Teichmüller spaces | ||||||
Journal or Publication Title: | Groups, Geometry and Dynamics | ||||||
Publisher: | European Mathematical Society Publishing House | ||||||
ISSN: | 1661-7207 | ||||||
Official Date: | 22 June 2020 | ||||||
Dates: |
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Volume: | 14 | ||||||
Number: | 2 | ||||||
Page Range: | pp. 607-652 | ||||||
DOI: | 10.4171/GGD/557 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Reuse Statement (publisher, data, author rights): | First published in: Bowditch Brian, Large-scale rank and rigidity of the Weil-Petersson metric. Groups Geom. Dyn. [Volume number (year)], [pages]. [doi]. © European Mathematical Society. | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Copyright Holders: | © European Mathematical Society | ||||||
Date of first compliant deposit: | 2 March 2020 | ||||||
Date of first compliant Open Access: | 2 March 2020 | ||||||
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