Le rang de certaines variétés closes
Annales de l'Institut Fourier, Volume 20 (1970) no. 1, p. 1-19

Let M be a closed and connected n-manifold with a locally free action ϕ of R n-1 on M, we prove : if π 1 (M) has no element of finite order the inclusion of a leaf of ϕ into M induces a monomorphism between the fundamentals groups.

As an application we prove that the rank of S 3 ×T n-3 is n-2.

Soit M une n-variété close et connexe munie d’une action localement libre ϕ de R n-1 sur M, on démontre : si π 1 (M) ne contient pas d’éléments d’ordre fini, l’inclusion de toute feuille de ϕ dans M induit un monomorphisme des groupes fondamentaux.

Comme application on prouve que le rang de S 3 ×T n-3 est n-2.

@article{AIF_1970__20_1_1_0,
     author = {Garan\c con, Maurice},
     title = {Le rang de certaines vari\'et\'es closes},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {20},
     number = {1},
     year = {1970},
     pages = {1-19},
     doi = {10.5802/aif.336},
     zbl = {0187.20402},
     mrnumber = {42 \#1142},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1970__20_1_1_0}
}
Garançon, Maurice. Le rang de certaines variétés closes. Annales de l'Institut Fourier, Volume 20 (1970) no. 1, pp. 1-19. doi : 10.5802/aif.336. http://www.numdam.org/item/AIF_1970__20_1_1_0/

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