Projective structures, grafting, and measured laminations

Details Projective structures, grafting, and measured laminations Projective structures, grafting, and measured laminations

2007-12-06

arxiv.org/abs/0712.0968v1

Mathematics

Differential Geometry

31 pages, 4 figures

Scientific paper

We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmuller space, complementing a result of Scannell-Wolf on grafting by a fixed lamination. This result is used to study the relationship between the complex-analytic and geometric coordinate systems for the space of complex projective ($\CP^1$) structures on a surface. We also study the rays in Teichmuller space associated to the grafting coordinates, obtaining estimates for extremal and hyperbolic length functions and their derivatives along these grafting rays.

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