The grafting map of Teichmüller space

Scannell, Kevin¹ ; Wolf, Michael²

¹ Department of Mathematics and Computer Science, Saint Louis University, Saint Louis, Missouri 63103
² Department of Mathematics, Rice University, Houston, Texas 77251

Journal of the American Mathematical Society, Tome 15 (2002) no. 4, pp. 893-927

Résumé

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.

Détail

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

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