2010/07/14 by Jonathan Pakianathan, Pakianathan, Jonathan, Ergün Yalçın +1
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary:20J06 #Secondary: 17B56
paper · pdf · doi:10.48550/arxiv.1007.2390
openalex publication_date 2010/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A central extension of the form E: 0 → V → G → W → 0, where V and W are elementary abelian 2-groups, is called Bockstein closed if the components qi ∈ H^*(W, \FF2) of the extension class of E generate an ideal which is closed under the Bockstein operator. In this paper, we study the cohomology ring of G when E is a Bockstein closed 2-power exact extension. The mod-2 cohomology ring of G has a simple form and it is easy to calculate. The main result of the paper is the calculation of the Bocksteins of the generators of the mod-2 cohomology ring using an Eilenberg-Moore spectral sequence. We also find an interpretation of the second page of the Bockstein spectral sequence in terms of a new cohomology theory that we define for Bockstein closed quadratic maps Q : W → V associated to the extensions E of the above form.