Cohomology Classification of Spaces with Free S3 Actions

2021/04/12 by Anju Kumari, Hemant Kumar Singh, Kumari, Anju +1
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Homotopy and Cohomology in Algebraic Topology #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2104.05377

Abstract

This paper gives the cohomology classification of finitistic spaces X equipped with free actions of the group G = S3 and the orbit space X/G is the integral or mod 2 cohomology quaternion projective space HPn. We have proved that X is the integral or mod 2 cohomology (4n+3)-sphere or the product of 3-sphere and quaternion projective space HPn. Similar results for G = S1 actions are also discussed.

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