On the cohomology of orbit space of free \pmb{${\ZZ}_{p}$}-actions on lens spaces

TL;DR

This paper determines the mod p cohomology ring of the orbit space resulting from a free a7 a7 p-action on a CW-complex with cohomology like a lens space, under specific divisibility conditions.

Contribution

It provides a complete description of the mod p cohomology ring of the orbit space for certain free a7 a7 p-actions on lens space-like complexes, extending previous knowledge.

Findings

Cohomology ring of the orbit space is explicitly computed.

Results depend on the divisibility condition p^2 a7 m.

Advances understanding of group actions on lens spaces.

Abstract

Let $G = \ZZ_p$, $p$ an odd prime, act freely on a finite-dimensional CW-complex $X$ with mod $p$ cohomology isomorphic to that of a lens space $L^{2m-1} (p;q_1,...,q_m)$. In this paper, we determine the mod $p$ cohomology ring of the orbit space $X/G$, when $p^2\nmid m$.