Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, 81:19

Localisation and colocalisation of KK-theory

Article

DOI: 10.1007/s12188-011-0050-7

Cite this article as:
Inassaridze, H., Kandelaki, T. & Meyer, R. Abh. Math. Semin. Univ. Hambg. (2011) 81: 19. doi:10.1007/s12188-011-0050-7

Abstract

The localisation of an R-linear triangulated category \(\mathcal{T}\) at S−1R for a multiplicatively closed subset S is again triangulated, and related to the original category by a long exact sequence involving a version of \(\mathcal{T}\) with coefficients in S−1R/R. We examine these theories and, under some assumptions, write the latter as an inductive limit of \(\mathcal{T}\) with torsion coefficients. Our main application is the case where \(\mathcal{T}\) is equivariant bivariant K-theory and R the ring of integers.

Keywords

LocalisationTriangulated categoryKK-theory

Mathematics Subject Classification (2000)

19K9919K3519D55

Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer 2011

Authors and Affiliations

  • Hvedri Inassaridze
    • 1
    • 2
  • Tamaz Kandelaki
    • 1
    • 2
  • Ralf Meyer
    • 3
  1. 1.A. Razmadze Mathematical InstituteTbilisi State UniversityTbilisiGeorgia
  2. 2.Tbilisi Centre for Mathematical SciencesTbilisiGeorgia
  3. 3.Mathematisches Institut and Courant Centre “Higher order structures”Georg-August Universität GöttingenGöttingenGermany