Weil–Petersson isometries via the pants complex

Brock, Jeffrey; Margalit, Dan

doi:10.1090/S0002-9939-06-08577-7

Weil–Petersson isometries via the pants complex
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by Jeffrey Brock and Dan Margalit PDF

Proc. Amer. Math. Soc. 135 (2007), 795-803 Request permission

Abstract:

We extend a theorem of Masur–Wolf which states that given a finite-area hyperbolic surface $S$, every isometry of the Teichmüller 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 times-punctured sphere, the once-punctured torus, and the twice-punctured torus.

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