Asymptotic cyclic cohomology

書誌事項

Asymptotic cyclic cohomology

Michael Puschnigg

(Lecture notes in mathematics, 1642)

Springer, c1996

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注記

Bibliography: p. [237]-238

Includes indexes

内容説明・目次

内容説明

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.

目次

The asymptotic homotopy category.- Algebraic de Rham complexes.- Cyclic cohomology.- Homotopy properties of X-complexes.- The analytic X-complex.- The asymptotic X-complex.- Asymptotic cyclic cohomology of dense subalgebras.- Products.- Exact sequences.- KK-theory and asymptotic cohomology.- Examples.

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詳細情報
  • NII書誌ID(NCID)
    BA29266863
  • ISBN
    • 3540619860
  • 出版国コード
    gw
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Berlin
  • ページ数/冊数
    xxiii, 238 p.
  • 大きさ
    24 cm
  • 分類
  • 親書誌ID
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