Units of ring spectra and their traces in algebraic K–theory

where $K (R)$ is the algebraic $K$ –theory and $THH (R)$ the topological Hochschild homology of $R$ . As a corollary we show that classes in $π_{i - 1} R$ not annihilated by the stable Hopf map $η \in π_{1}^{s} (S^{0})$ give rise to non-trivial classes in $K_{i} (R)$ for $i \geq 3$ .

Keywords

ring spectra, algebraic K-theory, topological Hochschild homology

Mathematical Subject Classification 2000

Primary: 19D55, 55P43

Secondary: 19D10, 55P48

References

Forward citations

Publication

Received: 25 November 2003

Revised: 21 April 2004

Accepted: 13 March 2004

Published: 22 April 2004

Proposed: Thomas Goodwillie

Seconded: Ralph Cohen, Haynes Miller

Authors

Christian Schlichtkrull
Department of Mathematics Oslo University PO Box 1053 Blindern NO-0316 Oslo Norway

Volume 8, issue 2 (2004)

Christian Schlichtkrull

Abstract