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Record Nr. |
UNINA9910154752903321 |
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Autore |
Douglas Ronald G. |
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Titolo |
C-Algebra Extensions and K-Homology. (AM-95), Volume 95 / / Ronald G. Douglas |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©1980 |
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ISBN |
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Descrizione fisica |
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1 online resource (94 pages) : illustrations |
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Collana |
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Annals of Mathematics Studies ; ; 228 |
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Disciplina |
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Soggetti |
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C*-algebras |
K-theory |
Algebra, Homological |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- Preface -- Chapter 1. An Overview -- Chapter 2. Ext as a Group -- Chapter 3. Ext as a Homotopy Functor -- Chapter 4. Generalized Homology Theory and Periodicity -- Chapter 5. Ext as K-Homology -- Chapter 6. Index Theorems snd Novikov's Higher Signatures -- References -- Index -- Index of Symbols -- Backmatter |
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Sommario/riassunto |
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Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained. |
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