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

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.