#### Volume 18, issue 4 (2014)

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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 ($2\pi$–) 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