Z_2 actions on complexes with three non-trivial cells

TL;DR

This paper investigates the possible fixed point sets of Z_2 group actions on specific cell complexes with particular cohomology rings, providing classifications and examples based on homological properties.

Contribution

It classifies fixed point sets of Z_2 actions on complexes with certain cohomology rings and relates these to homological properties, offering explicit examples.

Findings

Fixed point sets depend on homological properties of the complex.

Classification of fixed point sets for Z_2 actions on these complexes.

Examples illustrating each possible fixed point set case.

Abstract

In this paper, we study $Z_2$ actions on a cell complex X having the cohomology ring isomorphic to that of the wedge sum $P^2 (n) V S^{3n}$ or $S^n V S^{2n} V S^{3n}$. We determine the possible fixed point sets depending on whether or not X is totally non-homologous to zero in $X_{Z_2}$ and give examples realizing the possible cases.