Selecta Mathematica

, Volume 24, Issue 2, pp 1039–1091 | Cite as

The index map in algebraic K-theory

  • Oliver Braunling
  • Michael Groechenig
  • Jesse Wolfson


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.

Mathematics Subject Classification

Primary 19D55 Secondary 19K56 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Oliver Braunling
    • 1
  • Michael Groechenig
    • 2
  • Jesse Wolfson
    • 3
  1. 1.Department of MathematicsUniversität FreiburgFreiburgGermany
  2. 2.Department of MathematicsFreie Universität BerlinBerlinGermany
  3. 3.Department of MathematicsUniversity of California, IrvineIrvineUSA

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