Duke Mathematical Journal
- Duke Math. J.
- Volume 166, Number 8 (2017), 1517-1572.
Large-scale rank of Teichmüller space
Suppose that is either the mapping class group equipped with the word metric or Teichmüller space equipped with either the Teichmüller metric or the Weil–Petersson metric. We introduce a unified approach to study the coarse geometry of these spaces. We show that for any large box in there is a standard model of a flat in such that the quasi-Lipschitz image of a large sub-box is near the standard flat. As a consequence, we show that, for all these spaces, the geometric rank and the topological rank are equal. The methods are axiomatic and apply to a larger class of metric spaces.
Duke Math. J., Volume 166, Number 8 (2017), 1517-1572.
Received: 17 September 2013
Revised: 26 August 2016
First available in Project Euclid: 28 March 2017
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Eskin, Alex; Masur, Howard; Rafi, Kasra. Large-scale rank of Teichmüller space. Duke Math. J. 166 (2017), no. 8, 1517--1572. doi:10.1215/00127094-0000006X. https://projecteuclid.org/euclid.dmj/1490666574