A K-theoretic Refinement of Topological Realization of Unstable Algebras
نویسنده
چکیده
In this paper we propose and partially carry out a program to use K-theory to refine the topological realization problem of unstable algebras over the Steenrod algebra. In particular, we establish a suitable form of algebraic models for K-theory of spaces, called ψ-algebras, which give rise to unstable algebras by taking associated graded algebras mod p. The aforementioned problem is then split into (i) the algebraic problem of realizing unstable algebras as mod p associated graded of ψ-algebras and (ii) the topological problem of realizing ψ-algebras as K-theory of spaces. Regarding the algebraic problem, a theorem shows that every connected and even unstable algebra can be realized. We tackle the topological problem by obtaining a K-theoretic analogue of a theorem of Kuhn and Schwartz on the so-called Realization Conjecture.
منابع مشابه
Algebra over the Steenrod Algebra, Lambda-ring, and Kuhn’s Realization Conjecture
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