03983nam a22005895i 4500 978-3-031-59850-0 DE-He213 20251030112655.0 cr nn 008mamaa 240728s2024 sz | s |||| 0|eng d 9783031598500 978-3-031-59850-0 10.1007/978-3-031-59850-0 doi QA612.33 PBPD bicssc MAT002010 bisacsh PBPD thema Emerson, Heath. author. aut http://id.loc.gov/vocabulary/relators/aut 81439 An Introduction to C*-Algebras and Noncommutative Geometry [electronic resource] / by Heath Emerson. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Birkhäuser, 2024. XIII, 539 p. 27 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Birkhäuser Advanced Texts Basler Lehrbücher, 2296-4894 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. K-theory. 81440 Topology. 72917 Geometry, Differential. 69684 Dynamical systems. Functional analysis. K-Theory. 81441 Topology. 72917 Differential Geometry. 69686 Dynamical Systems. Functional Analysis. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031598494 Printed edition: 9783031598517 Printed edition: 9783031598524 Birkhäuser Advanced Texts Basler Lehrbücher, 2296-4894 80556 https://doi.org/10.1007/978-3-031-59850-0 ZDB-2-SMA ZDB-2-SXMS 61992 61992