Algebraic K-theory and topological spaces, by Michael Paluch

In this note we discuss the algebraic and topological K-theories of an admissible space X and demonstrate how one may recover the connective topological K-theory of X from the algebraic K-theory of a simplicial ring which encodes the topological structure of the Fréchet algebra of continuous functions on X. By considering Thomason's formulation of hypercohomology with coefficients in a presheaf of spectra, we present a new look at the familiar exponential sequence.


Michael Paluch <mike@math.ist.utl.pt>