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Weil-Petersson isometries via the pants complex

Jeffrey Brock·Dan Margalit
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Abstract

We extend a theorem of Masur and Wolf which says that given a hyperbolic surface S, every isometry of the Teichmuller space for S with the Weil-Petersson metric is induced by an element of the mapping class group for S. Our argument handles the previously untreated cases of the four-holed sphere, the one-holed torus, and the two-holed torus.

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Jeffrey Brock, Dan Margalit. 2004-12-27. Weil-Petersson isometries via the pants complex. https://arxiv.org/abs/math/0412499

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