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Published October 2, 2014 | Published
Journal Article Open

Asymptoticity of grafting and Teichmüller rays

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.

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.

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