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Word length in surface groups with characteristic generating sets

Calegari, Danny (2008) Word length in surface groups with characteristic generating sets. Proceedings of the American Mathematical Society, 136 (7). pp. 2631-2637. ISSN 0002-9939. doi:10.1090/S0002-9939-08-09443-4.

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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:© 2008 American Mathematical Society. The copyright for this article reverts to public domain after 28 years from publication. Received by the editors May 21, 2007. Article electronically published on February 29, 2008. I would like to thank Benson Farb for posing the question which this paper addresses, Chris Leininger for the observation mentioned in Remark 3.3, and the anonymous referee. This research was carried out while I was at the Tokyo Institute of Technology, hosted by Sadayoshi Kojima. I thank TIT and Professor Kojima for their hospitality.
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National Science FoundationDMS 0405491
Issue or Number:7
Record Number:CaltechAUTHORS:CALpams08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13295
Deposited On:06 Feb 2009 00:46
Last Modified:08 Nov 2021 22:36

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