03615nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001300153072001700166072002300183072001600206100007700222245010700299250001800406264007900424300004500503336002600548337002600574338003600600347002400636490006400660505047000724520143001194650001402624650001402638650002802652650002302680650002502703650001402728650001402742650002702756650002302783650002502806710003402831773002602865776003602891776003602927776003602963830006402999856004603063978-3-031-59850-0DE-He21320251030112655.0cr nn 008mamaa240728s2024    sz |    s    |||| 0|eng d  a97830315985007 a10.1007/978-3-031-59850-02doi 4aQA612.33 7aPBPD2bicssc 7aMAT0020102bisacsh 7aPBPD2thema1 aEmerson, Heath.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut13aAn Introduction to C*-Algebras and Noncommutative Geometryh[electronic resource] /cby Heath Emerson.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Birkhäuser,c2024.  aXIII, 539 p. 27 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aBirkhäuser Advanced Texts Basler Lehrbücher,x2296-48940 aAn 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.  aThis 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. 0aK-theory. 0aTopology. 0aGeometry, Differential. 0aDynamical systems. 0aFunctional analysis.14aK-Theory.24aTopology.24aDifferential Geometry.24aDynamical Systems.24aFunctional Analysis.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303159849408iPrinted edition:z978303159851708iPrinted edition:z9783031598524 0aBirkhäuser Advanced Texts Basler Lehrbücher,x2296-489440uhttps://doi.org/10.1007/978-3-031-59850-0