Chern Character

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 301)


One of the main themes of differential topology is: characteristic classes. The point is to define invariants of a topological or differentiable situation and then to calculate them. Many interesting invariants lie in the so-called K-groups. In the case of manifolds, for instance, these invariants are computed via the “Chern character”, which maps K-theory to the de Rham cohomology theory.


Vector Bundle Chem Character Cyclic Module Torsion Free Group Grothendieck Group 
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Bibliographical Comments on Chapter 8

  1. Milnor, J., Stasheff, J.D., Characteristic classes, Annals of Math. Studies 76, Princeton University Press, 1974.Google Scholar
  2. Karoubi, M., Homologie cyclique et K-théorie, Astérisque 149, 1987Google Scholar
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  4. Dennis, K., In search of a new homology theory, manuscript, 1976, never published. Dennis, K., Igusa, K., Hochschild homology and the second obstruction for pseudo-isotopy, Springer Lect. Notes in Math. 966 (1982), 7–58. 84m: 18014MathSciNetGoogle Scholar
  5. Quillen, D., Cyclic cohomology and algebra extensions. K-theory 3 (1989), 205–246.Google Scholar
  6. Kassel, C., Quand l’homologie cyclique périodique n’est pas la limite projective de l’homologie cyclique, K-theory 2 (1989a), 617–621MathSciNetzbMATHCrossRefGoogle Scholar
  7. Wang, X., Bivariant Chern character I, Proc. Symp. Pure Math. 51 (1990), 355–360.CrossRefGoogle Scholar
  8. Connes, A., Karoubi, M., Caractère multiplicatif d’un module de Fredholm, C. R. Acad. Sci. Paris Sér. A-B 299 (1984), 963–968, et K-theory 2 (1988), 431463. 90c:58174Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeCentre National de la Recherche ScientifiqueStrasbourgFrance

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