Large-scale rank and rigidity of the Weil-Petersson metric
type: Item
instance of: scholarly article
title: Large-scale rank and rigidity of the Weil-Petersson metric
zbMATH Open document ID: 1471.57013
DOI: 10.4171/GGD/557
author: B. H. Bowditch
published in: Groups, Geometry, and Dynamics
publication date: 2020-08-03T00:00:00Z
review text: This paper establishes several rigidity theorems regarding the coarse geometry of the Teichmüller space with Weil-Peterson metric, which the author calls the Weil-Peterson space. To do so, he construct a coarse median structure of the Weil-Peterson space, which in particular gives the coarse rank of the Weil-Peterson space originally proven by \textit{A. Eskin} et al. [Duke Math. J. 166, No. 8, 1517--1572 (2017; Zbl 1373.32012)]. Royden's theorem asserts that every isometry of the Teichmüller space with Teichmüller metric is given by a mapping class of the surface, and Masur and Wolf proved Royden's theorem with the Weil-Peterson metric. The author proves a coase version of Royden's theorem for the Weil-Peterson space, except when the complexity of the surface is low. The author also investigates the asymptotic cone of the Weil-Peterson space, and shows that it is uniquely determined by the base surface, similarly, for most of the cases.
reviewed by: Shinpei Baba
Mathematics Subject Classification ID: 57K20
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 7227240
zbMATH Keywords: quasi-isometry rigidity
zbMATH Keywords: Weil-Peterson metric
zbMATH Keywords: rank
zbMATH Keywords: coarse media
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/ggd/557
OpenAlex ID: W3009057984
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