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Asymptoticity of grafting and Teichmüller rays

Gupta, Subhojoy (2014) Asymptoticity of grafting and Teichmüller rays. Geometry and Topology, 18 (4). pp. 2127-2188. ISSN 1465-3060. doi:10.2140/gt.2014.18.2127.

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We show that any grafting ray in Teichmüller space determined by an arational lamination or a multicurve is (strongly) asymptotic to a Teichmüller geodesic ray. As a consequence the projection of a generic grafting ray to the moduli space is dense. We also show that the set of points in Teichmüller space obtained by integer (2π–) graftings on any hyperbolic surface projects to a dense set in the moduli space. This implies that the conformal surfaces underlying complex projective structures with any fixed Fuchsian holonomy are dense in the moduli space.

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Additional Information:© 2014 Mathematical Sciences Publishers. Received: 23 December 2012. Accepted: 3 February 2014. Published: 2 October 2014. Proposed: Benson Farb. Seconded: Jean-Pierre Otal, Yasha Eliashberg.
Subject Keywords:grafting rays, Teichmüller rays
Issue or Number:4
Classification Code:Mathematical Subject Classification 2010: Primary: 30F60 Secondary: 32G15, 57M50
Record Number:CaltechAUTHORS:20150212-151457941
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54794
Deposited By: Ruth Sustaita
Deposited On:13 Feb 2015 03:56
Last Modified:10 Nov 2021 20:38

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