Involution on the product of projective space and sphere

Dimpi; Hemant Kumar Singh

Involution on the product of projective space and sphere

Algebraic Topology 2023-03-30 v1

Authors: Dimpi , Hemant Kumar Singh

Abstract

Let $G=\mathbb{Z}_2$ act on a finite CW-complex $X$ having mod 2 cohomology isomorphic to the product of projective space and sphere $\mathbb{F}P^n\times \mathbb{S}^m,$ where $\mathbb{F}=\mathbb{R}$ or $\mathbb{C}.$ 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.

Keywords

involution projective space sphere free involution fixed point set orbit space borsuk-ulam

Cite

@article{arxiv.2303.16478,
  title  = {Involution on the product of projective space and sphere},
  author = {Dimpi and Hemant Kumar Singh},
  journal= {arXiv preprint arXiv:2303.16478},
  year   = {2023}
}

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