Finitistic Spaces with the Orbit Space FPⁿ x S^m

2023/06/06 by Anju Kumari, Hemant Kumar Singh, Kumari, Anju +1
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 55T10 #Secondary 57S99

paper · pdf · doi:10.48550/arxiv.2306.03738

openalex publication_date 2023/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G = S^d, d = 0, 1 or 3, act freely on a finitistic connected space X. This paper gives the cohomology classification of X if a mod 2 or rational cohomology of the orbit space X/G is isomorphic to the product of a projective space and sphere FPⁿ x S^m, where F = R, C or H, respectively. For a free involution on X, a lower bound of covering dimension of the coincidence set of a continuous map f: X -> R^k is also determined.

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