Cohomology Classification of Spaces with Free S3 Actions

Abstract

This paper gives the cohomology classification of finitistic spaces X equipped with free actions of the group G = S 3 and the orbit space X/G is the integral or mod 2 cohomology quaternion projective space HP n . We have proved that X is the integral or mod 2 cohomology S 4n+3 or S 3 × HP n . Similar results for G = S 1 actions are also discussed.