Indices of a Finitistic Space with Mod 2 Cohomology ℝPn × $$\\mathbb{S}^2$$S2

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 $$\\mathbb{S}^2$$S2. 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→Sn and $$\\mathbb{S}^n\\rightarrow{X}$$Sn→X. The covering dimensions of the coincidence sets of continuous maps X → ℝk are also determined.