Chromatic characteristic classes in ordinary group cohomology

Green, D.J.; Hunton, J.R.; Schuster, B.

Abstract

We study a family of subrings, indexed by the natural numbers, of the mod p cohomology of a finite group G. These subrings are based on a family of vn-periodic complex oriented cohomology theories and are constructed as rings of generalised characteristic classes. We identify the varieties associated to these subrings in terms of colimits over categories of elementary abelian subgroups of G, naturally interpolating between the work of Quillen on var(H* (BG)), the variety of the whole cohomology ring, and that of Green and Leary on the variety of the Chern subring, var(Ch(G)). Our subrings give rise to a ‘chromatic’ (co)filtration, which has both topological and algebraic definitions, of var(H* (BG)) whose final quotient is the variety var(Ch(G)).

Citation

Green, D., Hunton, J., & Schuster, B. (2003). Chromatic characteristic classes in ordinary group cohomology. Topology (Oxford), 42(1), 243-263. https://doi.org/10.1016/s0040-9383%2802%2900011-3

• Journal Article Type: Article
• Acceptance Date: Jan 10, 2002
• Online Publication Date: Apr 17, 2002
• Publication Date: 2003-01
• Deposit Date: Jul 22, 2019
• Journal: Topology
• Print ISSN: 0040-9383
• Electronic ISSN: 1879-3215
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 42
• Issue: 1
• Pages: 243-263
• DOI: https://doi.org/10.1016/s0040-9383%2802%2900011-3
• Public URL: https://durham-repository.worktribe.com/output/1326733