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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Asymptoticity of grafting and Teichmüller rays

Subhojoy Gupta

Geometry & Topology 18 (2014) 2127–2188
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 (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.

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