[Sur les variétés qui admettent des difféomorphismes de type quasi-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 , et dans ce cas le difféomorphisme est en fait d'Anosov, ou bien le goupe fondamental de M contient une copie de . Si n=4, alors Π1(M) contient une copie de , 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 , in which case the diffeomorphisms is Anosov, or else its fundamental group contains a copy of . If n=4 then Π1(M) contains a copy of , provided that the diffeomorphism is not Anosov.
Accepté le :
Publié le :
Jana Rodriguez Hertz 1 ; Raúl Ures 1 ; José L. Vieitez 1
@article{CRMATH_2002__334_4_321_0, author = {Jana Rodriguez Hertz and Ra\'ul Ures and Jos\'e L. Vieitez}, title = {On manifolds supporting {quasi-Anosov} diffeomorphisms}, journal = {Comptes Rendus. Math\'ematique}, pages = {321--323}, publisher = {Elsevier}, volume = {334}, number = {4}, year = {2002}, doi = {10.1016/S1631-073X(02)02260-4}, language = {en}, }
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 Sources :
☆ 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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