On manifolds supporting quasi-Anosov diffeomorphisms
[Sur les variétés qui admettent des difféomorphismes de type quasi-Anosov]
Rodriguez Hertz, Jana1 ; Ures, Raúl1 ; Vieitez, José L.1
1 CC 30, IMERL – Facultad de Ingenierı́a, Universidad de la República, Montevideo, Uruguay
Comptes Rendus. Mathématique, Tome 334 (2002) no. 4, pp. 321-323.

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.

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.

Reçu le :
Accepté le :
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DOI : 10.1016/S1631-073X(02)02260-4
Rodriguez Hertz, Jana 1 ; Ures, Raúl 1 ; Vieitez, José L. 1

1 CC 30, IMERL – Facultad de Ingenierı́a, Universidad de la República, Montevideo, Uruguay 
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Rodriguez Hertz, Jana; Ures, Raúl; Vieitez, José L. On manifolds supporting quasi-Anosov diffeomorphisms. Comptes Rendus. Mathématique, Tome 334 (2002) no. 4, pp. 321-323. doi : 10.1016/S1631-073X(02)02260-4. http://www.numdam.org/articles/10.1016/S1631-073X(02)02260-4/

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