000 03983nam a22005895i 4500
001 978-3-031-59850-0
003 DE-He213
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020 _a9783031598500
_9978-3-031-59850-0
024 7 _a10.1007/978-3-031-59850-0
_2doi
050 4 _aQA612.33
072 7 _aPBPD
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBPD
_2thema
100 1 _aEmerson, Heath.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981439
245 1 3 _aAn Introduction to C*-Algebras and Noncommutative Geometry
_h[electronic resource] /
_cby Heath Emerson.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2024.
300 _aXIII, 539 p. 27 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aBirkhäuser Advanced Texts Basler Lehrbücher,
_x2296-4894
505 0 _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.
520 _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.
650 0 _aK-theory.
_981440
650 0 _aTopology.
_972917
650 0 _aGeometry, Differential.
_969684
650 0 _aDynamical systems.
650 0 _aFunctional analysis.
650 1 4 _aK-Theory.
_981441
650 2 4 _aTopology.
_972917
650 2 4 _aDifferential Geometry.
_969686
650 2 4 _aDynamical Systems.
650 2 4 _aFunctional Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031598494
776 0 8 _iPrinted edition:
_z9783031598517
776 0 8 _iPrinted edition:
_z9783031598524
830 0 _aBirkhäuser Advanced Texts Basler Lehrbücher,
_x2296-4894
_980556
856 4 0 _uhttps://doi.org/10.1007/978-3-031-59850-0
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c61992
_d61992