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 \(\mathbb{S}^2\). 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 \(X\rightarrow\mathbb{S}^n\) and \(\mathbb{S}^n\rightarrow{X}\). The covering dimensions of the coincidence sets of continuous maps X → ℝk are also determined.
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The research is supported by R & D grant 2015–16 of the University of Delhi
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Singh, H.K., Singh, K.S. Indices of a Finitistic Space with Mod 2 Cohomology ℝPn × \(\mathbb{S}^2\). Indian J Pure Appl Math 50, 23–34 (2019). https://doi.org/10.1007/s13226-019-0304-0
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DOI: https://doi.org/10.1007/s13226-019-0304-0