Bockstein closed 2-group extensions and cohomology of quadratic maps

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dc.citation.epage60en_US
dc.citation.spage34en_US
dc.citation.volumeNumber357en_US
dc.contributor.authorPakianathan, J.en_US
dc.contributor.authorYalçın, E.en_US
dc.date.accessioned2015-07-28T12:04:45Z
dc.date.available2015-07-28T12:04:45Z
dc.date.issued2012-05-01en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractA 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,F 2) 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. © 2012 Elsevier Inc.en_US
dc.identifier.doi10.1016/j.jalgebra.2012.01.029en_US
dc.identifier.eissn1090-266X
dc.identifier.issn0021-8693
dc.identifier.urihttp://hdl.handle.net/11693/13146
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttps://doi.org/10.1016/j.jalgebra.2012.01.029en_US
dc.source.titleJournal of Algebraen_US
dc.subjectGroup cohomologyen_US
dc.subjectGroup extensionsen_US
dc.subjectQuadratic mapsen_US
dc.subjectSteenrod operationsen_US
dc.subjectprimary 20J06en_US
dc.subjectsecondary 17B56en_US
dc.titleBockstein closed 2-group extensions and cohomology of quadratic mapsen_US
dc.typeArticleen_US
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