×

Symmetric spectra and topological Hochschild homology. (English) Zbl 0938.55017

An unfortunate fact about symmetric spectra, is that stable equivalences are not measured by the homotopy groups. However, if the symmetric spectra in question are fibrant in the model structure defined in [J. Am. Math. Soc. 13, No. 1, 149-208 (2000; Zbl 0931.55006)], then a stable equivalence is exactly a map that induces an isomorphism on all homotopy groups. In this paper the author uses essentially the zero simplices of Bökstedt’s topological Hochschild homology construction to create a manageable fibrant replacement functor. As an application, Bökstedt’s definition of topological Hochschild homology is shown to be equivalent to what you get if you apply the Hochschild complex definition directly to a cofibrant ring spectrum.

MSC:

55P42 Stable homotopy theory, spectra
19D99 Higher algebraic \(K\)-theory
55U35 Abstract and axiomatic homotopy theory in algebraic topology

Citations:

Zbl 0931.55006
PDFBibTeX XMLCite
Full Text: DOI arXiv