Involution on the product of projective space and sphere

2023/03/29 by Hemant Kumar Singh, Dimpi, Singh, Hemant Kumar
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Primary 57S17 #Secondary 55M35

paper · pdf · doi:10.48550/arxiv.2303.16478

openalex publication_date 2023/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G=ℤ₂ act on a finite CW-complex X having mod 2 cohomology isomorphic to the product of projective space and sphere \mathbbFPⁿ× \mathbbS^m, where \mathbbF=ℝ or ℂ. In this paper, we have determined the connected fixed point sets and the orbit spaces of free involutions on X. As an application, we derive the Borsuk-Ulam type results.

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