On manifolds supporting quasi-Anosov diffeomorphisms

Jana Rodriguez Hertz; Raúl Ures; José L. Vieitez

doi:10.1016/S1631-073X(02)02260-4

On manifolds supporting quasi-Anosov diffeomorphisms
[Sur les variétés qui admettent des difféomorphismes de type quasi-Anosov]

Jana Rodriguez Hertz ¹ ; Raúl Ures ¹ ; José L. Vieitez ¹

¹ CC 30, IMERL – Facultad de Ingenierı́a, Universidad de la República, Montevideo, Uruguay

Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 321-323.

Abstract (VO)
Résumé

Let M be an n-dimensional manifold supporting a quasi-Anosov diffeomorphism. If n=3 then either $M = 𝕋^{3}$ , in which case the diffeomorphisms is Anosov, or else its fundamental group contains a copy of $ℤ^{6}$ . If n=4 then Π₁(M) contains a copy of $ℤ^{4}$ , provided that the diffeomorphism is not Anosov.

Soit M une variété différentiable de dimension n qui admet un difféomorphisme de type quasi-Anosov. Si n=3 alors on a l'altenative suivante, ou bien $M = 𝕋^{3}$ , et dans ce cas le difféomorphisme est en fait d'Anosov, ou bien le goupe fondamental de M contient une copie de $ℤ^{6}$ . Si n=4, alors Π₁(M) contient une copie de $ℤ^{4}$ , pourvu que le difféomorphisme ne soit pas d'Anosov.

Reçu le : 2001-12-19
Accepté le : 2002-01-07
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02260-4

Affiliations des auteurs :

Jana Rodriguez Hertz ¹ ; Raúl Ures ¹ ; José L. Vieitez ¹

¹ CC 30, IMERL – Facultad de Ingenierı́a, Universidad de la República, Montevideo, Uruguay

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     title = {On manifolds supporting {quasi-Anosov} diffeomorphisms},
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Jana Rodriguez Hertz; Raúl Ures; José L. Vieitez. On manifolds supporting quasi-Anosov diffeomorphisms. Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 321-323. doi : 10.1016/S1631-073X(02)02260-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02260-4/

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Cité par 2 documents. Sources : zbMATH

^☆ The first author was partially supported by a grant from PEDECIBA. The second author was partially supported by CONICYT, Fondo Clemente Estable.

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