Transactions of the American Mathematical Society

Author(s): Hirotaka Tamanoi
Journal: Trans. Amer. Math. Soc. 349 (1997), 1209-1237.
MSC (1991): Primary 55N22, 55P20, 55S25
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Abstract: Fundamental classes in $BP$

cohomology of Eilenberg-MacLane spaces are defined. The image of the Thom map from $BP$

cohomology to mod- $p$

cohomology is determined for arbitrary Eilenberg-MacLane spaces. This image is a polynomial subalgebra generated by infinitely many elements obtained by applying a maximum number of Milnor primitives to the fundamental class in mod- $p$

cohomology. This subalgebra in mod $p$

cohomology is invariant under the action of the Steenrod algebra, and it is annihilated by all Milnor primitives. We also show that $BP$

cohomology determines Morava $K$

cohomology for Eilenberg-MacLane spaces.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 55N22, 55P20, 55S25

Hirotaka Tamanoi
Affiliation: Institut des Hautes Études Scientifiques, 35 Route de Chartres, 91440 Bures-sur-Yvette, France
Address at time of publication: Department of Mathematics, University of California at Santa Cruz, Santa Cruz, California 95064
Email: tamanoi@cats.ucsc.edu

DOI: 10.1090/S0002-9947-97-01826-6
PII: S 0002-9947(97)01826-6
Keywords: $BP$ cohomology theory, $BP$ fundamental class, Eilenberg--Mac Lane spaces, Milnor primitives, Morava $K$ theory, Steenrod algebra, Thom map
Received by editor(s): October 5, 1995
Copyright of article: Copyright 1997, American Mathematical Society

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