Fixed point sets and orbit spaces of wedge of three spheres

Dimpi; Hemant Kumar Singh

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arXiv · 2303.16484

Fixed point sets and orbit spaces of wedge of three spheres

Dimpi·Hemant Kumar Singh

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Abstract

Let $X$ be a finite CW-complex having mod $p$ cohomology isomorphic to a wedge of three spheres $\mathbb{S}^n\vee \mathbb{S}^m \vee \mathbb{S}^l,~ 1\leq n \leq m \leq l$. The aim of this paper is to determine the fixed point sets of actions of the cyclic group of prime order on $X.$ We also classify the orbit spaces of free actions of $G=\mathbb{Z}_p, p$ a prime or $G=\mathbb{S}^d,~d=1,3,$ on $X$ and derive the Borsuk-Ulam type results.

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Dimpi, Hemant Kumar Singh. 2023-03-29. Fixed point sets and orbit spaces of wedge of three spheres. https://arxiv.org/abs/2303.16484

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