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Asymptotic Cyclic Cohomology [electronic resource] /
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.
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| Format: | Texto biblioteca |
| Language: | eng |
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Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
1996
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| Subjects: | Mathematics., Category theory (Mathematics)., Homological algebra., K-theory., Operator theory., Algebraic topology., Category Theory, Homological Algebra., Algebraic Topology., K-Theory., Operator Theory., |
| Online Access: | http://dx.doi.org/10.1007/BFb0094458 |
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KOHA-OAI-TEST:2071812018-07-30T23:37:31ZAsymptotic Cyclic Cohomology [electronic resource] / Puschnigg, Michael. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,1996.engThe 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.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.Mathematics.Category theory (Mathematics).Homological algebra.K-theory.Operator theory.Algebraic topology.Mathematics.Category Theory, Homological Algebra.Algebraic Topology.K-Theory.Operator Theory.Springer eBookshttp://dx.doi.org/10.1007/BFb0094458URN:ISBN:9783540495796 |
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| language |
eng |
| topic |
Mathematics. Category theory (Mathematics). Homological algebra. K-theory. Operator theory. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. K-Theory. Operator Theory. Mathematics. Category theory (Mathematics). Homological algebra. K-theory. Operator theory. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. K-Theory. Operator Theory. |
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Mathematics. Category theory (Mathematics). Homological algebra. K-theory. Operator theory. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. K-Theory. Operator Theory. Mathematics. Category theory (Mathematics). Homological algebra. K-theory. Operator theory. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. K-Theory. Operator Theory. Puschnigg, Michael. author. SpringerLink (Online service) Asymptotic Cyclic Cohomology [electronic resource] / |
| 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. |
| format |
Texto |
| topic_facet |
Mathematics. Category theory (Mathematics). Homological algebra. K-theory. Operator theory. Algebraic topology. Mathematics. Category Theory, Homological Algebra. Algebraic Topology. K-Theory. Operator Theory. |
| author |
Puschnigg, Michael. author. SpringerLink (Online service) |
| author_facet |
Puschnigg, Michael. author. SpringerLink (Online service) |
| author_sort |
Puschnigg, Michael. author. |
| title |
Asymptotic Cyclic Cohomology [electronic resource] / |
| title_short |
Asymptotic Cyclic Cohomology [electronic resource] / |
| title_full |
Asymptotic Cyclic Cohomology [electronic resource] / |
| title_fullStr |
Asymptotic Cyclic Cohomology [electronic resource] / |
| title_full_unstemmed |
Asymptotic Cyclic Cohomology [electronic resource] / |
| title_sort |
asymptotic cyclic cohomology [electronic resource] / |
| publisher |
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, |
| publishDate |
1996 |
| url |
http://dx.doi.org/10.1007/BFb0094458 |
| work_keys_str_mv |
AT puschniggmichaelauthor asymptoticcycliccohomologyelectronicresource AT springerlinkonlineservice asymptoticcycliccohomologyelectronicresource |
| _version_ |
1756268350199037952 |