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＜電子ブック＞
Asymptotic Cyclic Cohomology / by Michael Puschnigg
(Lecture Notes in Mathematics. ISSN:16179692 ; 1642)

版	1st ed. 1996.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1996
大きさ	XXIV, 244 p : online resource
著者標目	*Puschnigg, Michael author SpringerLink (Online service)
件　名	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
一般注記	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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