Indices of a Finitistic Space with Mod 2 Cohomology ℝPn × $$\mathbb{S}^2$$ S 2

Hemant Kumar Singh () and Konthoujam Somorjit Singh ()
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Hemant Kumar Singh: University of Delhi
Konthoujam Somorjit Singh: University of Delhi

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 1, 23-34

Abstract: Abstract Let G = ℤ2 act freely on a finitistic space X with mod 2 cohomology ring isomorphic to the product of a real projective space and 2-sphere $$\mathbb{S}^2$$ S 2 . In this paper, we determine the Conner and Floyd’s mod 2 cohomology index and the Volovikov’s numerical index of X. Using these indices, we discuss the nonexistence of equivariant maps $$X\rightarrow\mathbb{S}^n$$ X → S n and $$\mathbb{S}^n\rightarrow{X}$$ S n → X . The covering dimensions of the coincidence sets of continuous maps X → ℝk are also determined.

Keywords: Free action; finitistic space; Leray-Serre spectral sequence; index; covering dimension (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0304-0

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