The image of the Thom map for Eilenberg-MacLane spaces

Author:
Hirotaka Tamanoi

Journal:
Trans. Amer. Math. Soc. **349** (1997), 1209-1237

MSC (1991):
Primary 55N22, 55P20, 55S25

MathSciNet review:
1401530

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Abstract: Fundamental classes in cohomology of Eilenberg-MacLane spaces are defined. The image of the Thom map from cohomology to mod- 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- 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 Eilenberg-MacLane spaces.

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Additional Information

**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:
https://doi.org/10.1090/S0002-9947-97-01826-6

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

Article copyright:
© Copyright 1997
American Mathematical Society