Asymptoticity of grafting and Teichmüller rays I

Details Asymptoticity of grafting and Teichmüller rays I Asymptoticity of grafting and Teichmüller rays I

2011-09-25

arxiv.org/abs/1109.5365v1

Mathematics

Geometric Topology

51 pages, 21 figures

Scientific paper

We show that any grafting ray in Teichm\"{u}ller space determined by an arational lamination or a multi-curve is (strongly) asymptotic to a Teichm\"{u}ller geodesic ray. As a consequence the projection of a generic grafting ray to moduli space is dense. We also show that the set of points in Teichm\"{u}ller space obtained by integer (2\pi-) graftings on any hyperbolic surface projects to a dense set, which implies that complex projective surfaces with any fixed Fuchsian holonomy are dense in moduli space.

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