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Asymptotic Cyclic Cohomology

  • Book
  • © 1996

Overview

Authors:
  1. Michael Puschnigg
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1642)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxiii
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  2. The asymptotic homotopy category

    • Michael Puschnigg
    Pages 1-18

  3. Algebraic de Rham complexes

    • Michael Puschnigg
    Pages 19-26

  4. Cyclic cohomology

    • Michael Puschnigg
    Pages 27-39

  5. Homotopy properties of X-complexes

    • Michael Puschnigg
    Pages 40-58

  6. The analytic X-complex

    • Michael Puschnigg
    Pages 59-96

  7. The asymptotic X-complex

    • Michael Puschnigg
    Pages 97-117

  8. Asymptotic cyclic cohomology of dense subalgebras

    • Michael Puschnigg
    Pages 118-126

  9. Products

    • Michael Puschnigg
    Pages 127-157

  10. Exact sequences

    • Michael Puschnigg
    Pages 158-181

  11. KK-theory and asymptotic cohomology

    • Michael Puschnigg
    Pages 182-201

  12. Examples

    • Michael Puschnigg
    Pages 202-231

  13. Back Matter

    Pages 232-238
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Keywords

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.

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