Fixed point free actions of spheres and equivariant maps

Free Actions of Compact Lie Groups on Manifolds

“…For example, L. W. Cusick [12] showed that if a finite group G acts freely on a product of spheres of even dimensions, X ¼ S 2n 1  ⋯  S 2n k , then then G must be isomorphic to a group of the type  r 2 , for some r ≤ k: Concerning on free actions of a finite group  p , p prime, and the circle group S 1 on a product of spheres S m  S n , Dotzel et al [13] showed the following classification results according to Theorems 3. Using the same techniques, it is shown in [14] similar results regarding the action of groups S 1 and S 3 on the product of spheres, considering both rational and mod 2 coefficients.…”