Title: Subalgebras of group cohomology defined by infinite loop spaces
Authors: John R. Hunton
Bj"orn Schuster
MSC: 20J06 55N20 55P47 (primary), 55R40 19A22 55P60 (secondary)
arXiv: math.AT/0112169
Addresses: The Department of Mathematics and Computer Science, University of
Leicester, University Road, Leicester, LE1 7RH, England
Department of Mathematics, University of Wuppertal, Gaussstr.~20,
D-42097 Wuppertal, Germany.
Abstract:
We study natural subalgebras Ch_E(G) of group cohomology defined in terms
of infinite loop spaces E and give representation theoretic descriptions of
those based on QS^0 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;F_p) 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 HF_p which is non-trivial in homotopy. We
also extend the constructions to define subalgebras of H^*(X;F_p) for any
space X; when X is finite we show that the subalgebras Ch_{E(n)}(X)
give a natural unstable chromatic filtration of H^*(X;F_p).