Fixed point free actions of spheres and equivariant maps

The concept of index and co-index a paracompact Hausdorff space X equipped with free involutions relative to the antipodal action on spheres were introduced by Conner Floyd [2] . In this paper, we extend notion for G -spaces , where is finitistic = S 1 (with complex multiplication) 3 quaternionic multiplication). We prove that less than or equal mod 2 cohomology also compute ring orbit / whose same as product n × m ≤ Using these cohomological calculations, obtain some Borsuk-Ulam type results.