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      On nilpotent ideals in the cohomology ring of a finite group

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      Author(s)
      Pakianathan, J.
      Yalçin, E.
      Date
      2003
      Source Title
      Topology
      Print ISSN
      0040-9383
      Volume
      42
      Issue
      5
      Pages
      1155 - 1183
      Language
      English
      Type
      Article
      Item Usage Stats
      209
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      Abstract
      In 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.
      Keywords
      Cohomology of groups
      Essential cohomology
      Group action on graphs
      Permalink
      http://hdl.handle.net/11693/24443
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/S0040-9383(02)00086-1
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