The image of the Thom map for EilenbergMacLane spaces
Author:
Hirotaka Tamanoi
Journal:
Trans. Amer. Math. Soc. 349 (1997), 12091237
MSC (1991):
Primary 55N22, 55P20, 55S25
MathSciNet review:
1401530
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Abstract: Fundamental classes in cohomology of EilenbergMacLane spaces are defined. The image of the Thom map from cohomology to mod cohomology is determined for arbitrary EilenbergMacLane 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 cohomology. This subalgebra in mod cohomology is invariant under the action of the Steenrod algebra, and it is annihilated by all Milnor primitives. We also show that cohomology determines Morava cohomology for EilenbergMacLane spaces.
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Additional Information
Hirotaka Tamanoi
Affiliation:
Institut des Hautes Études Scientifiques, 35 Route de Chartres, 91440 BuressurYvette, 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:
http://dx.doi.org/10.1090/S0002994797018266
PII:
S 00029947(97)018266
Keywords:
$BP$ cohomology theory,
$BP$ fundamental class,
EilenbergMac Lane spaces,
Milnor primitives,
Morava $K$ theory,
Steenrod algebra,
Thom map
Received by editor(s):
October 5, 1995
Article copyright:
© Copyright 1997
American Mathematical Society
