Fixed point sets and orbit spaces of wedge of three spheres

Abstract

Let $X$ be a finite CW-complex having mod $p$ cohomology isomorphic to a wedge of three spheres ${\mathbb{S}}^n\vee {\mathbb{S}}^m\vee {\mathbb{S}}^l,1\le n\le m\le l$. 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.