Vol. 57, No. 2, 1975

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Multiplicative operations in BPBP

Douglas Conner Ravenel

Vol. 57 (1975), No. 2, 539–543

One of the present computational difficulties in complex cobordism theory is the lack of a known algebra splitting of BPBP, the algebra of stable cohomology operations for the Brown-Peterson cohomology theory, analogous to the splitting isomorphism

M U∗M U ≈ M U ∗(pt)⊗ S

where S is the Landweber-Novikov algebra. S has the added advantage of being a cocommutative Hopf algebra over Z. This paper does not remove this difficulty, but we will show that the monoid of multiplicative operations in BPBP, (i.e. those operations which induce ring endomorphisms on BPX for any space X), which we will denote by Γ(BP), has a submonoid analogous to the monoid of multiplicative operations in S.

Mathematical Subject Classification 2000
Primary: 55G25
Secondary: 14L05
Received: 4 December 1974
Published: 1 April 1975
Douglas Conner Ravenel