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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Word length in surface groups with characteristic generating sets
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by Danny Calegari PDF
Proc. Amer. Math. Soc. 136 (2008), 2631-2637 Request permission

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
  • 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