Asymptoticity of grafting and Teichmüller rays

Gupta, Subhojoy

doi:10.2140/gt.2014.18.2127

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Asymptoticity of grafting and Teichmüller rays

Subhojoy Gupta

Geometry & Topology 18 (2014) 2127–2188

DOI: 10.2140/gt.2014.18.2127

Abstract

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 ( $2 π$ –) 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.

Keywords

grafting rays, Teichmüller rays

Mathematical Subject Classification 2010

Primary: 30F60

Secondary: 32G15, 57M50

References

Publication

Received: 23 December 2012

Accepted: 3 February 2014

Published: 2 October 2014

Proposed: Benson Farb

Seconded: Jean-Pierre Otal, Yasha Eliashberg

Authors

Subhojoy Gupta
Division of Physics, Mathematics and Astronomy California Institute of Technology 1200 E. California Blvd. Mathematics 253-37 Pasadena, CA 91125 USA and Center for Quantum Geometry of Moduli Spaces Ny Munkegade 118 Aarhus C 8000 Denmark

Volume 18, issue 4 (2014)