Journal of the Mathematical Society of Japan

Cohomology algebra of orbit spaces of free involutions on lens spaces

Mahender SINGH

Full-text: Open access

Abstract

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 $L_p^{2m-1}$ $(q_1,\dots,q_m)$. 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 maps $\mathbb{S}^n \to X$.

Article information

Source
J. Math. Soc. Japan, Volume 65, Number 4 (2013), 1055-1078.

Dates
First available in Project Euclid: 24 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1382620185

Digital Object Identifier
doi:10.2969/jmsj/06541055

Mathematical Reviews number (MathSciNet)
MR3127816

Zentralblatt MATH identifier
1292.57030

Subjects
Primary: 57S17: Finite transformation groups
Secondary: 55R20: Spectral sequences and homology of fiber spaces [See also 55Txx] 55M20: Fixed points and coincidences [See also 54H25]

Keywords
cohomology algebra finitistic space index of involution Leray spectral sequence orbit space Smith-Gysin sequence

Citation

SINGH, Mahender. Cohomology algebra of orbit spaces of free involutions on lens spaces. J. Math. Soc. Japan 65 (2013), no. 4, 1055--1078. doi:10.2969/jmsj/06541055. https://projecteuclid.org/euclid.jmsj/1382620185


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