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

Schlichtkrull, Christian¹

¹ Department of Mathematics, Oslo University, PO Box 1053, Blindern, NO-0316 Oslo, Norway

Geometry & topology, Tome 8 (2004) no. 2, pp. 645-673.

Résumé

Let $G{L}_1\left(R\right)$ be the units of a commutative ring spectrum $R$. In this paper we identify the composition

where $K\left(R\right)$ is the algebraic $K$–theory and $THH\left(R\right)$ the topological Hochschild homology of $R$. As a corollary we show that classes in ${\pi }_{i-1}R$ not annihilated by the stable Hopf map $\eta \in {\pi }_1^s\left(S^0\right)$ give rise to non-trivial classes in $K_i\left(R\right)$ for $i\ge 3$.

Détail

DOI : 10.2140/gt.2004.8.645

Keywords: ring spectra, algebraic K-theory, topological Hochschild homology

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