Algebra over the Steenrod Algebra, Lambda-ring, and Kuhn’s Realization Conjecture
نویسنده
چکیده
In this paper we study the relationships between operations in K-theory and ordinary mod p cohomology. In particular, conditions are given under which the mod p associated graded ring of a filtered λ-ring is an unstable algebra over the Steenrod algebra. This result partially extends to the algebraic setting a topological result of Atiyah about operations on K-theory and mod p cohomology for torsionfree spaces. It is also shown that any polynomial algebra that is an algebra over the Steenrod algebra can be realized as the mod p associated graded of a filtered λ-ring. Another observation is that Atiyah’s result gives rise to a K-theoretic analogue of Kuhn’s Realization Conjecture concerning the size of spaces in cohomology.
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