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Abstract
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We study the asymptotic geometry of Teichmüller space equipped with the
Weil–Petersson metric. In particular, we provide a characterization of the canonical
finest pieces in the tree-graded structure of the asymptotic cone of Teichmüller
space along the same lines as a similar characterization for right angled Artin groups
and for mapping class groups. As a corollary of the characterization, we complete the
thickness classification of Teichmüller spaces for all surfaces of finite type, thereby
answering questions of Behrstock, Druţu and Mosher, and Brock and Masur. In
particular, we prove that Teichmüller space of the genus-two surface with one
boundary component (or puncture) is the only Teichmüller space which is thick of
order two.
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Keywords
Teichmüller space, asymptotic cone, thickness
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Mathematical Subject Classification 2010
Primary: 30F60, 20F69
Secondary: 20F65, 20F67
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Publication
Received: 24 November 2014
Revised: 22 January 2015
Accepted: 2 February 2015
Published: 10 December 2015
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