Word length in surface groups with characteristic generating sets
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- by Danny Calegari
- Proc. Amer. Math. Soc. 136 (2008), 2631-2637
- DOI: https://doi.org/10.1090/S0002-9939-08-09443-4
- Published electronically: February 29, 2008
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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.References
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Bibliographic Information
- Danny Calegari
- Affiliation: Department of Mathematics, Caltech, Pasadena, California 91125
- MR Author ID: 605373
- Email: dannyc@its.caltech.edu
- Received by editor(s): May 21, 2007
- Published electronically: February 29, 2008
- Communicated by: Daniel Ruberman
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2631-2637
- MSC (2000): Primary 57M07
- DOI: https://doi.org/10.1090/S0002-9939-08-09443-4
- MathSciNet review: 2390536