© 1996

Asymptotic Cyclic Cohomology

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1642)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Michael Puschnigg
    Pages 1-18
  3. Michael Puschnigg
    Pages 19-26
  4. Michael Puschnigg
    Pages 27-39
  5. Michael Puschnigg
    Pages 40-58
  6. Michael Puschnigg
    Pages 59-96
  7. Michael Puschnigg
    Pages 97-117
  8. Michael Puschnigg
    Pages 118-126
  9. Michael Puschnigg
    Pages 127-157
  10. Michael Puschnigg
    Pages 158-181
  11. Michael Puschnigg
    Pages 182-201
  12. Michael Puschnigg
    Pages 202-231
  13. Back Matter
    Pages 232-238

About this book


The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups.


Cohomology De Rham cohomology Homotopy K-theory cohomology group cohomology theory homology

Bibliographic information

  • Book Title Asymptotic Cyclic Cohomology
  • Authors Michael Puschnigg
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-61986-4
  • eBook ISBN 978-3-540-49579-6
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XXIV, 244
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Category Theory, Homological Algebra
    Algebraic Topology
    Operator Theory
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