C-Algebra Extensions and K-Homology. (AM-95), Volume 95 / / Ronald G. Douglas

• Autore: Douglas Ronald G.
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1980
• Descrizione fisica: 1 online resource (94 pages) : illustrations
• Disciplina: 512/.55
• Soggetto topico: C*-algebras; K-theory; Algebra, Homological
• Soggetto non controllato: Addition; Affine transformation; Algebraic topology; Atiyah–Singer index theorem; Automorphism; Banach algebra; Bijection; Boundary value problem; Bundle map; C*-algebra; Calculation; Cardinal number; Category of abelian groups; Characteristic class; Chern class; Clifford algebra; Coefficient; Cohomology; Compact operator; Completely positive map; Contact geometry; Continuous function; Corollary; Diagram (category theory); Diffeomorphism; Differentiable manifold; Differential operator; Dimension (vector space); Dimension function; Dimension; Direct integral; Direct proof; Eigenvalues and eigenvectors; Equivalence class; Equivalence relation; Essential spectrum; Euler class; Exact sequence; Existential quantification; Fiber bundle; Finite group; Fredholm operator; Fredholm; Free abelian group; Fundamental class; Fundamental group; Hardy space; Hermann Weyl; Hilbert space; Homological algebra; Homology (mathematics); Homomorphism; Homotopy; Ideal (ring theory); Inner automorphism; Irreducible representation; K-group; K-theory; Lebesgue space; Locally compact group; Maximal compact subgroup; Michael Atiyah; Monomorphism; Morphism; Natural number; Natural transformation; Normal operator; Operator algebra; Operator norm; Operator theory; Orthogonal group; Pairing; Piecewise linear manifold; Polynomial; Pontryagin class; Positive and negative parts; Positive map; Pseudo-differential operator; Quaternion; Quotient algebra; Self-adjoint operator; Self-adjoint; Simply connected space; Smooth structure; Special case; Stein manifold; Strong topology; Subalgebra; Subgroup; Subset; Summation; Tangent bundle; Theorem; Todd class; Topology; Torsion subgroup; Unitary operator; Universal coefficient theorem; Variable (mathematics); Von Neumann algebra
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: -Algebra Extensions and K-Homology. (AM-95), Volume 95
• ISBN: 1-4008-8146-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154752903321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 95.