The grafting map of Teichmüller space |
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| Authors: | Kevin P. Scannell Michael Wolf |
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| Affiliation: | Department of Mathematics and Computer Science, Saint Louis University, Saint Louis, Missouri 63103 ; Department of Mathematics, Rice University, Houston, Texas 77251 |
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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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