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An un-delooped version of algebraic K-theory
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
FB Mathematik, Universität Osnabrück.
FB Mathematik, Universität Osnabrück.
FB Mathematik, Universität Bielefeld.
1992 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 79, no 3, p. 255-270Article in journal (Refereed) Published
Abstract [en]

Problems working with the Segal operations in algebraic K-theory of spaces-constructed by F. Waldhausen (1982)-arose from the absence of a nice groupcompletion on the category level. H. Grayson and D. Gillet (1987) introduced a combinatorial model G. for K-theory of exact categories. For dealing with K-theory of spaces we need an extension wG. of their result to the context of categories with cofibrations and weak equivalences. Our main result is that in the presence of a suspension functor-as in the case of retractive spaces-the wG. construction on the category of prespectra is an un-delooped version of the K-theory of the original category. In a sequel to this paper we show that Grayson's formula (1988) for Segal operations works as intended.

Place, publisher, year, edition, pages
1992. Vol. 79, no 3, p. 255-270
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-4399DOI: 10.1016/0022-4049(92)90053-IISI: A1992HZ50800004Scopus ID: 2-s2.0-38249012563Local ID: 258b8040-b6a5-11db-abff-000ea68e967bOAI: oai:DiVA.org:ltu-4399DiVA, id: diva2:977272
Note
Godkänd; 1992; 20070207 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Gunnarsson, Thomas

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