04605nam 22008415 450 991087805880332120251217130004.09783031598500(electronic bk.)978303159849410.1007/978-3-031-59850-0(MiAaPQ)EBC31570252(Au-PeEL)EBL31570252(CKB)33469257700041(MiAaPQ)EBC31571722(Au-PeEL)EBL31571722(DE-He213)978-3-031-59850-0(OCoLC)1450835111(EXLCZ)993346925770004120240728d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAn Introduction to C*-Algebras and Noncommutative Geometry /by Heath Emerson1st ed. 2024.Cham :Springer International Publishing :Imprint: Birkhäuser,2024.1 online resource (548 pages)Birkhäuser Advanced Texts Basler Lehrbücher,2296-4894Print version: Emerson, Heath An Introduction to C*-Algebras and Noncommutative Geometry Cham : Springer International Publishing AG,c2024 9783031598494 Includes bibliographical references.An introduction to C*-algebras -- An Introduction to Index Theory and Noncommutative Geometry -- Spectral Theory and Representation -- Positivity, Representations, Tensor Products and Ideals in C*-algebras -- Module theory of C*-algebras -- Morita Equivalence -- Topological K-theory and Clifford Algebras -- K-theory for C*algebras -- The Index Theorem of Atiyah and Singer -- K-homology and Noncommutative Geometry -- An Introduction to KK-theory -- Bibliography.This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes’ Noncommuntative Riemannian geometry. Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details.Birkhäuser Advanced Texts Basler Lehrbücher,2296-4894K-theoryTopologyGeometry, DifferentialDynamicsFunctional analysisK-TheoryTopologyDifferential GeometryDynamical SystemsFunctional AnalysisC*-àlgebresthubGeometria diferencial no commutativathubTeoria espectral (Matemàtica)thubK-teoriathubTeoria de l'índex (Matemàtica)thubLlibres electrònicsthubK-theory.Topology.Geometry, Differential.Dynamics.Functional analysis.K-Theory.Topology.Differential Geometry.Dynamical Systems.Functional Analysis.C*-àlgebresGeometria diferencial no commutativaTeoria espectral (Matemàtica)K-teoriaTeoria de l'índex (Matemàtica)512.55Emerson Heath1762086MiAaPQMiAaPQMiAaPQ9910878058803321-Algebras and Noncommutative Geometry4471240UNINA