Asymptoticity of grafting and Teichmuller rays

作者：Gupta Subhojoy^*

来源：Geometry and Topology, 2014, 18(4): 2127-2188.

DOI：10.2140/gt.2014.18.2127

We show that any grafting ray in Teichmuller space determined by an arational lamination or a multicurve is (strongly) asymptotic to a Teichmuller 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 Teichmuller 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.

• 出版日期2014