Metric properties of the group of area preserving diffeomorphisms
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- by Michel Benaim and Jean-Marc Gambaudo
- Trans. Amer. Math. Soc. 353 (2001), 4661-4672
- DOI: https://doi.org/10.1090/S0002-9947-01-02808-2
- Published electronically: June 14, 2001
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Abstract:
Area preserving diffeomorphisms of the 2-disk which are identity near the boundary form a group ${\mathcal D}_2$ which can be equipped, using the $L^2$-norm on its Lie algebra, with a right invariant metric. With this metric the diameter of ${\mathcal D}_2$ is infinite. In this paper we show that ${\mathcal D}_2$ contains quasi-isometric embeddings of any finitely generated free group and any finitely generated abelian free group.References
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Bibliographic Information
- Michel Benaim
- Affiliation: Université de Cergy Pontoise, Laboratoire de Mathématiques, 2, avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France
- Email: benaim@math.u-cergy.fr
- Jean-Marc Gambaudo
- Affiliation: Université de Bourgogne, Laboratoire de Topologie, UMR CNRS 5584, B.P. 47870-21078-Dijon Cedex, France
- Received by editor(s): April 11, 2000
- Received by editor(s) in revised form: October 30, 2000
- Published electronically: June 14, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 4661-4672
- MSC (1991): Primary 20F36, 58B05, 58B25, 76A02
- DOI: https://doi.org/10.1090/S0002-9947-01-02808-2
- MathSciNet review: 1851187