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Flots d'Anosov sur les 3-variétés fibrées en cercles

Published online by Cambridge University Press:  19 September 2008

Etienne Ghys
Etienne Ghys
Affiliation:
Université des Sciences et Techniques de LilleI, 59650 Villeneuve d'Ascq, France
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Abstract

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We consider Anosov flows on closed 3-manifolds which are circle bundles. Our main result is that, up to a finite covering, these flows are topologically equivalent to the geodesic flow of a suface of constant negative curvature. The same method shows that, if M is a closed hyperbolic manifold of any dimension, all the geodesic flows which correspond to different metrics on M and which are of Anosov type are topologically equivalent.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 1 , March 1984 , pp. 67 - 80
Copyright
Copyright © Cambridge University Press 1984

References

BIBLIOGRAPHIE

[1]Anosov, D. V.. Geodesic flows on closed riemannian manifolds with negative curvature. Proc. Steklov Institute, 90 (1967).Google Scholar
[2]Camacho, C. & Lins, A.. Teoria geométrica das folheações. IMPA, Projeto Euclides (1979).Google Scholar
[3]Franks, J.. Anosov diffeomorphisms. Proc. Sympos. Pure Math. (Amer. Math. Soc.), 14 (1970), 61–91.CrossRefGoogle Scholar
[4]Franks, J. & Williams, B.. Anomalous Anosov flows. Springer Lecture Notes in Math. n°819, 158–174.Google Scholar
[5]Goodman, S.. Dehn surgery on Anosov flows (à paraître).Google Scholar
[6]Gromov, M.. Three remarks on geodesic dynamics and fundamental group. Preprint.Google Scholar
[7]Handel, M. & Thurston, W.. Anosov flows on new three manifolds. Invent. Math. 59 (2) (1980), 95–103.CrossRefGoogle Scholar
[8]Klingenberg, W.. Riemannian manifolds with geodesic flow of Anosov type. Ann. of Math. 99 (1974), 1–13.CrossRefGoogle Scholar
[9]Levitt, G.. Feuilletages des variétés de dimension trois qui sont des fibrés en cercles. Comment. Math. Helv. 53 (1978), 572–594.CrossRefGoogle Scholar
[10]Palmeira, C. F. B.. Open manifolds foliated by planes. Ann. of Math. (1978), 107, 109–131.CrossRefGoogle Scholar
[11]Plante, J.. Foliations of 3-manifolds with solvable fundamental group. Invent. Math. 51 (1979), 219–230.CrossRefGoogle Scholar
[12]Plante, J.. Anosov flows, transversally affine foliations and a conjecture of Verjovsky. Preprint.Google Scholar
[13]Plante, J. & Thurston, W.. Anosov flows and the fundamental group. Topology 11 (1972), 147–150.CrossRefGoogle Scholar
[14]Reeb, G.. Les espaces localement numériques non séparés et leurs applications à un problème classique. Colloque de Topologie de Strasbourg, 1955, (proceedings).Google Scholar
[15]Roussarie, R.. Plongements dans les variétés et classification des feuilletages sans holonomie. Inst. Hautes Etudes Set. Publ Math. 43 (1974), 101–142.CrossRefGoogle Scholar
[16]Tomter, P.. Anosov flows on infra-homogeneous spaces. Proc. Symp. Pure Math. 14 (1970), 299–328.CrossRefGoogle Scholar
[17]Thurston, W., Foliations on 3-manifolds which are circle bundles. Thesis, Berkeley 1972.Google Scholar
[18]Thurston, W.. The geometry and topology of 3-manifolds. Lecture notes, Princeton University.Google Scholar
[19]Verjovsky, A.. Codimension one Anosov flows. Bol. Soc. Mexicana, 19 (1974), pp. 49–77.Google Scholar