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  • Book
  • © 1996

Asymptotic Cyclic Cohomology

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
  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

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.

Keywords

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

Bibliographic Information

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions