The index map in algebraic K-theory

• Oliver Braunling ^[1] ; Michael Groechenig ^[2] ; Jesse Wolfson ^[3]
  1. [1] University of Fribourg

     University of Fribourg

     Friburgo, Suiza

     
  2. [2] Freie Universität Berlin
  3. [3] University of California

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 2, 2018, págs. 1039-1091
• Idioma: inglés
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• Resumen

  • In this paper we provide a detailed description of the K-theory torsor constructed by S. Saito for a Tate R-module, and its analogue for general idempotent complete exact categories. We study the classifying map of this torsor in detail, construct an explicit simplicial model, and link it to the index theory of Fredholm operators. The torsor is also related to canonical central extensions of loop groups. More precisely, we compare the K-theory torsor to previously studied dimension and determinant torsors.