2001/12/17 by John Hunton, John R. Hunton, Hunton, John R. +3
Mathematics · #20J06 (primary) #55P47 (secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:20J06 #msc:55P47
paper · pdf · doi:10.48550/arxiv.math/0112169
20 pages
arxiv created 2001/12/17 · openalex publication_date 2001/12/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study natural subalgebras ChE(G) of group cohomology defined in terms of infinite loop spaces E and give representation theoretic descriptions of those based on QS0 and the Johnson-Wilson theories E(n). We describe the subalgebras arising from the Brown-Peterson spectra BP and as a result give a simple reproof of Yagita's theorem that the image of BP^*(BG) in H^*(BG;Fp) is F-isomorphic to the whole cohomology ring; the same result is shown to hold with BP replaced by any complex oriented theory E with a map of ring spectra from E to HFp which is non-trivial in homotopy. We also extend the constructions to define subalgebras of H^*(X;Fp) for any space X; when X is finite we show that the subalgebras ChE(n)(X) give a natural unstable chromatic filtration of H^*(X;Fp).