<E-Book>
Asymptotic Cyclic Cohomology / by Michael Puschnigg
(Lecture Notes in Mathematics. ISSN:16179692 ; 1642)
Edition | 1st ed. 1996. |
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Publisher | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
Year | 1996 |
Size | XXIV, 244 p : online resource |
Authors | *Puschnigg, Michael author SpringerLink (Online service) |
Subjects | LCSH:Algebra, Homological LCSH:Algebraic topology LCSH:K-theory LCSH:Operator theory FREE:Category Theory, Homological Algebra FREE:Algebraic Topology FREE:K-Theory FREE:Operator Theory |
Notes | 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 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 HTTP:URL=https://doi.org/10.1007/BFb0094458 |
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E-Book | Location | Media type | Volume | Call No. | Status | Reserve | Comments | ISBN | Printed | Restriction | Designated Book | Barcode No. |
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E-Book | オンライン | 電子ブック |
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Springer eBooks | 9783540495796 |
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電子リソース |
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EB00209171 |
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