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| Authors: | Hirotaka Tamanoi |
| Affiliation: | Institut des Hautes Études Scientifiques, 35 Route de Chartres, 91440 Bures-sur-Yvette, France |
| 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. |
| Keywords: | $BP$ cohomology theory $BP$ fundamental class Eilenberg--Mac Lane spaces Milnor primitives Morava $K$ theory Steenrod algebra Thom map |
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