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arxiv: math/0412499 · v1 · submitted 2004-12-27 · 🧮 math.DG · math.GT

Weil-Petersson isometries via the pants complex

classification 🧮 math.DG math.GT
keywords torusweil-peterssonargumentcasesclasscomplexelementevery
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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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