Weil–petersson Isometries via the Pants Complex
نویسندگان
چکیده
We extend a theorem of Masur and Wolf which says that given a 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-holed sphere and the torus with one or two holes.
منابع مشابه
Pants decompositions and the Weil-Petersson metric
Since notions of coarse geometry and quasi-isometries were first introduced by M. Gromov, many studies of geometry have been renovated with its rough perspective. In this note we give an expository account of results of [Br] and of joint work of the author with Benson Farb [BF] that apply such a coarse point of view to the Weil-Petersson metric on Teichmüller space. A natural graph of pants dec...
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