06172nam 22018015 450 991015475290332120190708092533.01-4008-8146-310.1515/9781400881468(CKB)3710000000620139(SSID)ssj0001651243(PQKBManifestationID)16426223(PQKBTitleCode)TC0001651243(PQKBWorkID)14782694(PQKB)11732407(MiAaPQ)EBC4738508(DE-B1597)467950(OCoLC)1024046392(OCoLC)979728672(DE-B1597)9781400881468(EXLCZ)99371000000062013920190708d2016 fg engurcnu||||||||txtccrC*-Algebra Extensions and K-Homology. (AM-95), Volume 95 /Ronald G. DouglasPrinceton, NJ : Princeton University Press, [2016]©19801 online resource (94 pages) illustrationsAnnals of Mathematics Studies ;228Bibliographic Level Mode of Issuance: Monograph0-691-08265-0 0-691-08266-9 Includes bibliographical references and index.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 -- BackmatterRecent 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.Annals of mathematics studies ;Number 95.C*-algebrasK-theoryAlgebra, HomologicalAddition.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.C*-algebras.K-theory.Algebra, Homological.512/.55Douglas Ronald G., 54969DE-B1597DE-B1597BOOK9910154752903321-Algebra Extensions and K-Homology. (AM-95), Volume 952988187UNINA