Isoperimetric inequalities for the handlebody groups
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- by Ursula Hamenstädt and Sebastian Hensel PDF
- Trans. Amer. Math. Soc. 365 (2013), 5313-5327 Request permission
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
- Martin R. Bridson and Karen Vogtmann, On the geometry of the automorphism group of a free group, Bull. London Math. Soc. 27 (1995), no. 6, 544–552. MR 1348708, DOI 10.1112/blms/27.6.544
- M. Bridson, K. Vogtmann, The Dehn function of $\textrm {Aut}(F_n)$ and $\textrm {Out}(F_n)$, arXiv: 1011.1506.
- U. Hamenstädt, Geometry of the mapping class group II: A biautomatic structure, arXiv:0912.0137.
- Ursula Hamenstädt and Sebastian Hensel, The geometry of the handlebody groups I: distortion, J. Topol. Anal. 4 (2012), no. 1, 71–97. MR 2914874, DOI 10.1142/S1793525312500070
- M. Handel, L. Mosher, Lipschitz retraction and distortion for subgroups of $\textrm {Out}(F_n)$, arXiv:1009.0518.
- Allen Hatcher, Homological stability for automorphism groups of free groups, Comment. Math. Helv. 70 (1995), no. 1, 39–62. MR 1314940, DOI 10.1007/BF02565999
- Allen Hatcher and Karen Vogtmann, Isoperimetric inequalities for automorphism groups of free groups, Pacific J. Math. 173 (1996), no. 2, 425–441. MR 1394399
- Howard Masur, Measured foliations and handlebodies, Ergodic Theory Dynam. Systems 6 (1986), no. 1, 99–116. MR 837978, DOI 10.1017/S014338570000331X
- H. A. Masur and Y. N. Minsky, Geometry of the complex of curves. II. Hierarchical structure, Geom. Funct. Anal. 10 (2000), no. 4, 902–974. MR 1791145, DOI 10.1007/PL00001643
- Darryl McCullough, Twist groups of compact $3$-manifolds, Topology 24 (1985), no. 4, 461–474. MR 816525, DOI 10.1016/0040-9383(85)90015-1
- Lee Mosher, Mapping class groups are automatic, Ann. of Math. (2) 142 (1995), no. 2, 303–384. MR 1343324, DOI 10.2307/2118637
- John R. Stallings, Whitehead graphs on handlebodies, Geometric group theory down under (Canberra, 1996) de Gruyter, Berlin, 1999, pp. 317–330. MR 1714852
- Bronisław Wajnryb, Mapping class group of a handlebody, Fund. Math. 158 (1998), no. 3, 195–228. MR 1663329, DOI 10.4064/fm-158-3-195-228
Additional Information
- Ursula Hamenstädt
- Affiliation: Mathematisches Institut der Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
- MR Author ID: 243357
- 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
- MR Author ID: 938076
- ORCID: 0000-0002-9369-4173
- Email: loplop@math.uni-bonn.de, hensel@math.uchicago.edu
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3074375