The grafting map of Teichmüller space

Scannell, Kevin; Wolf, Michael

doi:10.1090/S0894-0347-02-00395-8

The grafting map of Teichmüller space
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by Kevin P. Scannell and Michael Wolf

J. Amer. Math. Soc. 15 (2002), 893-927

DOI: https://doi.org/10.1090/S0894-0347-02-00395-8

Published electronically: May 16, 2002

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Abstract:

Grafting is a method of obtaining new projective structures from a hyperbolic structure, basically by gluing a flat cylinder into a surface along a closed geodesic in the hyperbolic structure, or by limits of that procedure. This induces a map of Teichmüller space to itself. We prove that this map is a homeomorphism by analyzing harmonic maps between pairs of grafted surfaces. As a corollary we obtain bending coordinates for the Bers embedding of Teichmüller space.

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