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The Conner-Floyd map for formal A-modules. (English) Zbl 0623.55001

A generalization of the Conner-Floyd map from complex cobordism to complex K-theory is constructed for formal A-modules. Let BP be the spectrum representing Brown-Peterson cohomology and let E be the Adams summand of complex K-theory. The BP version of the Conner-Floyd map is a map of spectra BP\(\to E\) which induces a natural equivalence \(BP_*X \otimes_{BP_*} E_*\simeq E_*X\). The author describes the corresponding generalization of the map \((BP_*,BP_*BP)\to (E_*,E_*E)\) induced by the Conner-Floyd map and computes the generalization of \(E_*E\). This is employed to confirm a conjecture of Ravenel.
Reviewer: Y.Furukawa

MSC:

55N22 Bordism and cobordism theories and formal group laws in algebraic topology
55T25 Generalized cohomology and spectral sequences in algebraic topology
55P42 Stable homotopy theory, spectra
14L05 Formal groups, \(p\)-divisible groups
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