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

 

Word length in surface groups with characteristic generating sets


Author: Danny Calegari
Journal: Proc. Amer. Math. Soc. 136 (2008), 2631-2637
MSC (2000): Primary 57M07
Published electronically: February 29, 2008
MathSciNet review: 2390536
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Abstract: A subset of a group is characteristic if it is invariant under every automorphism of the group. We study word length in fundamental groups of closed hyperbolic surfaces with respect to characteristic generating sets consisting of a finite union of orbits of the automorphism group, and show that the translation length of any element with a nonzero crossing number is positive, and bounded below by a constant depending only (and explicitly) on a bound on the crossing numbers of generating elements. This answers a question of Benson Farb.


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Additional Information

Danny Calegari
Affiliation: Department of Mathematics, Caltech, Pasadena, California 91125
Email: dannyc@its.caltech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09443-4
PII: S 0002-9939(08)09443-4
Received by editor(s): May 21, 2007
Published electronically: February 29, 2008
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.