|
Metric properties of the group of area preserving diffeomorphisms
Author(s):
Michel
Benaim;
Jean-Marc
Gambaudo
Journal:
Trans. Amer. Math. Soc.
353
(2001),
4661-4672.
MSC (1991):
Primary 20F36, 58B05, 58B25, 76A02
Posted:
June 14, 2001
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Area preserving diffeomorphisms of the 2-disk which are identity near the boundary form a group  which can be equipped, using the  -norm on its Lie algebra, with a right invariant metric. With this metric the diameter of  is infinite. In this paper we show that  contains quasi-isometric embeddings of any finitely generated free group and any finitely generated abelian free group.
References:
-
- 1.
- ARNOLD, V. AND KHESIN, B. Topological methods in hydrodynamics. Applied Mathematical Sciences, 125, (1998). MR 99b:58002
- 2.
- BANYAGA, A.: On the group of diffeomorphisms preserving an exact symplectic form, in Differential topology, Varenna (1976), 5-9. MR 83g:58006
- 3.
- BIRMAN, J. Braids, Links and Mapping Class Groups. Annals of Math. Studies 82, Princeton University Press, (1974) Erratum, 1975. MR 51:11477; MR 54:13894
- 4.
- CALABI, E.: On the group of automorphisms of a symplectic manifold, in Problems in analysis, Symposium in honor of S. Bochner, R. C. Gunning, Ed., Princeton Univ. Press, Princeton (1970), 1-26. MR 50:3268
- 5.
- EBIN, D. G. AND MARSDEN, J.: Groups of diffeomorphisms and the notion of an incompressible fluid, Ann. of Math. 92, (1970), 102-163.
- 6.
- ELIASHBERG, Y. AND RATIU, T.: The diameter of the symplectomorphism group is infinite, Invent. Math. 103, (1991), 327-340. MR 92a:58018
- 7.
- FATHI, A.: Transformations et homéomorphismes préservant la mesure. Systèmes dynamiques minimaux., Thèse Orsay (1980).
- 8.
- GAMBAUDO, J.-M. AND GHYS, ´E.: Enlacements asymptotiques, Topology 36, (1997), 1355-1379. MR 98f:57050
- 9.
- GAMBAUDO, J.-M. AND LAGRANGE, M.: Topological lower bounds on the distance between area preserving diffeomorphisms, Bol. Soc. Brasil. Mat. 31, (2000), 1-19. CMP 2000:12
- 10.
- GHYS, ´E. AND DE LA HARPE, P. Sur les groupes hyperboliques d'après Mikhael Gromov, Ghys, É and de la Harpe, eds., Progress in Mathematics 83, Birkhauser, (1990). MR 92f:53050
- 11.
- KINGMAN, J. F. C.: The ergodic theory of subadditive stochastic processes, J. Royal Stat. Soc., 30, (1968), 499-510. MR 40:8114
- 12.
- MURASUGI, K. Knot theory and its applications. Translated from the 1993 Japanese original by Bohdan Kurpita. Birkhäuser Boston, Inc., Boston, (1996). MR 97g:57011
- 13.
- SHNIRELMAN, A.: The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid, Matem. Sbornik 128, (1985), 82-109; English transl: Math. USSR, Sbornik 56 (1987), 79-105. MR 87d:58034
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(1991):
20F36, 58B05, 58B25, 76A02
Retrieve articles in all Journals with MSC
(1991):
20F36, 58B05, 58B25, 76A02
Additional 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
DOI:
10.1090/S0002-9947-01-02808-2
PII:
S 0002-9947(01)02808-2
Keywords:
Area preserving diffeomorphisms,
braids,
free groups,
quasi-isometry
Received by editor(s):
April 11, 2000
Received by editor(s) in revised form:
October 30, 2000
Posted:
June 14, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org