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First European Congress of Mathematics Paris, July 6–10, 1992 pp 213–241Cite as

The Cyclotomic Trace in Algebraic K-Theory

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Part of the book series: Progress in Mathematics ((PM,volume 120))

Abstract

This paper reviews the relations between algebraic K-theory and topological cyclic homology given by cyclotomic trace. If one, very superficially, views algebraic K-theory as classifying invertible matrices, then the cyclotomic trace records the trace of all powers of matrices. In a more relevant formulation, the topological cyclic homology has the same relationship to Bökstedt’s topological Hochschild homology as Connes’ cyclic homology has to Hochschild homology, and the cyclotomic trace is a topological cyclic version of the Dennis trace map.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Aarhus, DK-8000, Aarhus C, Denmark

    Ib Madsen

Authors
  1. Ib Madsen
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Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques Fondamentales, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    Anthony Joseph  & Rudolf Rentschler  & 

  2. The Weizmann Institute of Science, Rehovot, 76100, Israel

    Anthony Joseph

  3. Mathématiques, Université de Paris-Sud, Bâtiment 425, 91405, Orsay Cedex, France

    Fulbert Mignot

  4. Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    François Murat

  5. Laboratoire de Statistique Médicale, Université Paris V, 45, rue des Saints Pères, 75270, Paris Cedex 06, France

    Bernard Prum

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© 1994 Birkhäuser Verlag

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Madsen, I. (1994). The Cyclotomic Trace in Algebraic K-Theory. In: Joseph, A., Mignot, F., Murat, F., Prum, B., Rentschler, R. (eds) First European Congress of Mathematics Paris, July 6–10, 1992. Progress in Mathematics, vol 120. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9112-7_9

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  • DOI: https://doi.org/10.1007/978-3-0348-9112-7_9

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9912-3

  • Online ISBN: 978-3-0348-9112-7

  • eBook Packages: Springer Book Archive

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