Asymptotic Cyclic Cohomology

  • Authors
  • Michael Puschnigg
Book

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

Introduction

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.

Keywords

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

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0094458
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-61986-4
  • Online ISBN 978-3-540-49579-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book