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October, 2013 Cohomology algebra of orbit spaces of free involutions on lens spaces
Mahender SINGH
J. Math. Soc. Japan 65(4): 1055-1078 (October, 2013). DOI: 10.2969/jmsj/06541055


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 $\mathbb{S}^n \to X$.


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Mahender SINGH. "Cohomology algebra of orbit spaces of free involutions on lens spaces." J. Math. Soc. Japan 65 (4) 1055 - 1078, October, 2013.


Published: October, 2013
First available in Project Euclid: 24 October 2013

zbMATH: 1292.57030
MathSciNet: MR3127816
Digital Object Identifier: 10.2969/jmsj/06541055

Primary: 57S17
Secondary: ‎55M20 , 55R20

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

Rights: Copyright © 2013 Mathematical Society of Japan


Vol.65 • No. 4 • October, 2013
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