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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

   
 
 

 

Distortion and Tits alternative in smooth mapping class groups


Authors: Sebastian Hurtado and Emmanuel Militon
Journal: Trans. Amer. Math. Soc. 371 (2019), 8587-8623
MSC (2010): Primary 37C85, 57S25
DOI: https://doi.org/10.1090/tran/7476
Published electronically: February 27, 2019
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Abstract: In this article, we study the smooth mapping class group of a surface $ S$ relative to a given Cantor set, that is, the group of isotopy classes of orientation-preserving smooth diffeomorphisms of $ S$ which preserve this Cantor set. When the Cantor set is the standard ternary Cantor set, we prove that this group does not contain any distorted element. Moreover, we prove a weak Tits alternative for these groups.


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Additional Information

Sebastian Hurtado
Affiliation: Math Department, University of Chicago, Chicago, Illinois 60615

Emmanuel Militon
Affiliation: Laboratoire de Mathématiques J.A. Dieudonné, Université Côte d’Azur, Parc Valrose, 06102 Nice cedex 02, France

DOI: https://doi.org/10.1090/tran/7476
Received by editor(s): June 29, 2017
Received by editor(s) in revised form: November 23, 2017, and November 28, 2017
Published electronically: February 27, 2019
Article copyright: © Copyright 2019 Sebastian Hurtado and Emmanuel Militon