On the Existence of Free Action of S3 on Certain Finitistic Mod P Cohomology Spaces

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Authors

  • Jaspreet Kaur
     Department of Mathematics, University of Delhi, Delhi - 110007 ,IN
  • Hemant Kumar Singh
     Department of Mathematics, University of Delhi, Delhi - 110007 ,IN

Keywords:

Free Action, Finitistic Space, Leray-Serre Spectral Sequence, Mod p Cohomology Algebra.
Algebra

Abstract

In this paper we investigate the possibility of free actions of G = S3 on a finitistic mod p cohomology (sphere, real projective space or lens space) X. If X is a mod 2 cohomology k-sphere, then it is observed that G can act freely on X only if k = 4n − 1. In this case, with the canonical free G-action on S4m−1, we prove that there exist no equivariant map from S4n−1 to X if m > n. If X is a mod 2 cohomology real projective space or mod p cohomology lens space, p an odd prime then we prove that G can not act freely on X.

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Published

2015-12-01

How to Cite

Kaur, J., & Singh, H. K. (2015). On the Existence of Free Action of S<sup>3</sup> on Certain Finitistic Mod P Cohomology Spaces. The Journal of the Indian Mathematical Society, 82(3-4), 97–106. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/1685

Issue

Volume 82, Issue 3-4, July-December 2015

Section

Articles

License

Copyright (c) 2015 Jaspreet Kaur, Hemant Kumar Singh

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

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