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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weil-Petersson isometries via the pants complex


Authors: Jeffrey Brock and Dan Margalit
Journal: Proc. Amer. Math. Soc. 135 (2007), 795-803
MSC (2000): Primary 32G15; Secondary 32M99
Published electronically: September 11, 2006
MathSciNet review: 2262875
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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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Additional Information

Jeffrey Brock
Affiliation: Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912
Email: brock@math.brown.edu

Dan Margalit
Affiliation: Department of Mathematics, University of Utah, 155 S 1440 East, Salt Lake City, Utah 84112-0090
Email: margalit@math.utah.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08577-7
PII: S 0002-9939(06)08577-7
Keywords: Teichm\"uller space, Weil--Petersson metric, isometries, mapping class groups
Received by editor(s): January 18, 2005
Received by editor(s) in revised form: October 14, 2005
Published electronically: September 11, 2006
Additional Notes: The first author was partially supported by NSF grant number 0354288.
The second author was partially supported by an NSF postdoctoral fellowship and a VIGRE postdoctoral position under NSF grant number 0091675 to the University of Utah.
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2006 American Mathematical Society