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Transactions of the American Mathematical Society

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

 
 

 

Isoperimetric inequalities for the handlebody groups


Authors: Ursula Hamenstädt and Sebastian Hensel
Journal: Trans. Amer. Math. Soc. 365 (2013), 5313-5327
MSC (2010): Primary 20F65, 57M07
DOI: https://doi.org/10.1090/S0002-9947-2012-05808-9
Published electronically: December 27, 2012
MathSciNet review: 3074375
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the mapping class group of a handlebody $ V$ of genus at least $ 2$ has a Dehn function of at most exponential growth type.


References [Enhancements On Off] (What's this?)

  • [BV95] M. Bridson, K. Vogtmann, On the geometry of the group of automorphisms of a free group, Bull. London Math. Soc. 27 (1995), 544-525. MR 1348708 (96j:20050)
  • [BV10] M. Bridson, K. Vogtmann, The Dehn function of $ {\rm Aut}(F_n)$ and $ {\rm Out}(F_n)$, arXiv:
    1011.1506.
  • [H09b] U. Hamenstädt, Geometry of the mapping class group II: A biautomatic structure, arXiv:0912.0137.
  • [HH11] U. Hamenstädt, S. Hensel, The geometry of the handlebody groups I: Distortion, J. Topol. Anal. 4 (2012), no. 1, 71-97. MR 2914874
  • [HM10] M. Handel, L. Mosher, Lipschitz retraction and distortion for subgroups of $ {\rm Out}(F_n)$, arXiv:1009.0518.
  • [Ha95] A. Hatcher, Homological stability for automorphism groups of free groups, Comm. Math. Helv. 70 (1995), 39-62. MR 1314940 (95k:20030)
  • [HV96] A. Hatcher, K. Vogtmann, Isoperimetric inequalities for automorphism groups of free groups, Pacific J. Math. 173 (1996), no. 2, 425-441. MR 1394399 (97f:20045)
  • [M86] H. Masur, Measured foliations and handlebodies, Erg. Th. & Dynam. Sys. 6 (1986), 99-116. MR 837978 (87i:57011)
  • [MM00] H. Masur, Y. Minsky, Geometry of the complex of curves II: Hierarchical structure, Geom. Funct. Anal. 10 (2000), 902-974. MR 1791145 (2001k:57020)
  • [McC85] D. McCullough, Twist groups of compact $ 3$-manifolds, Topology 24 (1985), no. 4, 461-474. MR 816525 (87a:57019)
  • [Mo95] L. Mosher, Mapping class groups are automatic, Ann. of Math. (2) 142 (1995), no. 2, 303-384. MR 1343324 (96e:57002)
  • [St99] J. Stallings, Whitehead graphs on handlebodies, Geometric group theory down under (Canberra, 1996), 317-330, de Gruyter, Berlin, 1999. MR 1714852 (2001i:57028)
  • [Wa98] B. Wajnryb, Mapping class group of a handlebody, Fund. Math. 158 (1998), no. 3, 195-228. MR 1663329 (2000a:20075)

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Additional Information

Ursula Hamenstädt
Affiliation: Mathematisches Institut der Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
Email: ursula@math.uni-bonn.de

Sebastian Hensel
Affiliation: Mathematisches Institut der Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
Address at time of publication: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Email: loplop@math.uni-bonn.de, hensel@math.uchicago.edu

DOI: https://doi.org/10.1090/S0002-9947-2012-05808-9
Received by editor(s): November 4, 2011
Received by editor(s) in revised form: February 7, 2012
Published electronically: December 27, 2012
Additional Notes: Both authors were partially supported by the Hausdorff Center, Bonn and the Hausdorff Institut, Bonn. The second author was supported by the Max-Planck Institut für Mathematik, Bonn
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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