On nilpotent ideals in the cohomology ring of a finite group

dc.citation.epage1183en_US
dc.citation.issueNumber5en_US
dc.citation.spage1155en_US
dc.citation.volumeNumber42en_US
dc.contributor.authorPakianathan, J.en_US
dc.contributor.authorYalçin, E.en_US
dc.date.accessioned2016-02-08T10:29:29Z
dc.date.available2016-02-08T10:29:29Z
dc.date.issued2003en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractIn this paper we find upper bounds for the nilpotency degree of some ideals in the cohomology ring of a finite group by studying fixed point free actions of the group on suitable spaces. The ideals we study are the kernels of restriction maps to certain collections of proper subgroups. We recover the Quillen-Venkov lemma and the Quillen F-injectivity theorem as corollaries, and discuss some generalizations and further applications.We then consider the essential cohomology conjecture, and show that it is related to group actions on connected graphs. We discuss an obstruction for constructing a fixed point free action of a group on a connected graph with zero "k-invariant" and study the class related to this obstruction. It turns out that this class is a "universal essential class" for the group and controls many questions about the groups essential cohomology and transfers from proper subgroups. © 2002 Elsevier Science Ltd. All rights reserved.en_US
dc.identifier.doi10.1016/S0040-9383(02)00086-1en_US
dc.identifier.issn0040-9383
dc.identifier.urihttp://hdl.handle.net/11693/24443
dc.language.isoEnglishen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/S0040-9383(02)00086-1en_US
dc.source.titleTopologyen_US
dc.subjectCohomology of groupsen_US
dc.subjectEssential cohomologyen_US
dc.subjectGroup action on graphsen_US
dc.titleOn nilpotent ideals in the cohomology ring of a finite groupen_US
dc.typeArticleen_US

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