Cohomology algebra of orbit spaces of free involutions on lens spaces

Details Cohomology algebra of orbit spaces of free involutions on lens spaces Cohomology algebra of orbit spaces of free involutions on lens spaces

2008-05-19

arxiv.org/abs/0805.2865v6

Mathematics

Algebraic Topology

16 pages, to appear in Journal of the Mathematical Society of Japan

Scientific paper

Let $G$ be a group acting continuously on a space $X$ and let $X/G$ be its orbit space. Determining the topological or cohomological type of the orbit space $X/G$ is a classical problem in the theory of transformation groups. In this paper, we consider this problem for cohomology lens spaces. Let $X$ be a finitistic space having the mod 2 cohomology algebra of the lens space $L_p^{2m-1}(q_1,...,q_m)$. Then we classify completely the possible mod 2 cohomology algebra of orbit spaces of arbitrary free involutions on $X$. We also give examples of spaces realizing the possible cohomology algebras. In the end, we give an application of our results to non-existence of $\mathbb{Z}_2$-equivariant map $\mathbb{S}^n \to X$.

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