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The grafting map of Teichmuller space

Kevin P. Scannell·Michael Wolf
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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 Teichmuller 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 Teichmuller space.

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Kevin P. Scannell, Michael Wolf. 1998-10-13. The grafting map of Teichmuller space. https://arxiv.org/abs/math/9810082

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