Le rang de certaines variétés closes

Garançon, Maurice

Annales de l'Institut Fourier, Tome 20 (1970) no. 1, pp. 1-19.

Soit $M$ une $n$-variété close et connexe munie d’une action localement libre $\varphi$ de ${\mathbf{R}}^{n-1}$ sur $M$, on démontre : si ${\pi }_1\left(M\right)$ ne contient pas d’éléments d’ordre fini, l’inclusion de toute feuille de $\varphi$ dans $M$ induit un monomorphisme des groupes fondamentaux.

Comme application on prouve que le rang de $S^3\times T^{n-3}$ est $n-2$.

Let $M$ be a closed and connected $n$-manifold with a locally free action $\varphi$ of ${\mathbf{R}}^{n-1}$ on $M$, we prove : if ${\pi }_1\left(M\right)$ has no element of finite order the inclusion of a leaf of $\varphi$ into $M$ induces a monomorphism between the fundamentals groups.

As an application we prove that the rank of $S^3\times T^{n-3}$ is $n-2$.

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