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- catalog abstract "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.".
- catalog contributor b10161867.
- catalog created "c1996.".
- catalog date "1996".
- catalog date "c1996.".
- catalog dateCopyrighted "c1996.".
- catalog description "Contents: Introduction -- The asymptotic homotopy category -- Algebraic de Rham complexes -- Cyclic cohomology -- Homotopy properties of X-complexes -- The analytic X-complexes.-The asymptotic X-complex -- Asymptotic cohomology of dense subalgebras -- Products -- Exact sequences -- K-Theory and asymptotic cohomology -- Examples.".
- catalog description "Includes bibliographical references (p.[237]-238) and index.".
- catalog description "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.".
- catalog extent "xiii, 238 p. ;".
- catalog identifier "3540619860 (softcover : alk. paper)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1642.".
- catalog isPartOf "Lecture notes in mathematics ; 1642".
- catalog issued "1996".
- catalog issued "c1996.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog subject "510 s 514/.23 21".
- catalog subject "Homology theory.".
- catalog subject "Index theory (Mathematics)".
- catalog subject "K-theory.".
- catalog subject "KK-theory.".
- catalog subject "Mathematics.".
- catalog subject "Operator theory.".
- catalog subject "QA3 .L28 no. 1642 QA612.3".
- catalog tableOfContents "Contents: Introduction -- The asymptotic homotopy category -- Algebraic de Rham complexes -- Cyclic cohomology -- Homotopy properties of X-complexes -- The analytic X-complexes.-The asymptotic X-complex -- Asymptotic cohomology of dense subalgebras -- Products -- Exact sequences -- K-Theory and asymptotic cohomology -- Examples.".
- catalog title "Asymptotic cyclic cohomology / Michael Puschnigg.".
- catalog type "text".