Subalgebras of group cohomology defined by infinite loop spaces
نویسندگان
چکیده
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 QS 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 E → 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).
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