Laboratoire de Mathématiques Jean Leray

Richard G. Swan has shown: For any finite periodic group $G$ with the period $2d$ there is a free and cellular action $G\times X(2d-1)\longrightarrow X(2d-1),$ where $X(2d-1)$ is a $(2d-1)$-dimensional $CW$-complex with the homotopy type of the sphere $\mathbb{S}^{2d-1}$.}

The first part of this talk presents some results on free actions of finite groups on homotopy spheres. In the second one, we aim to generalize the Swan's result above on some discrete infinite groups.