MARC Record from Library of Congress

LEADER: 02748cam a22002774a 4500
001 2010487128
003 DLC
005 20110325083608.0
008 100809s2009 sz b 001 0 eng c
010 $a 2010487128
020 $a9783037190616
020 $a3037190612
035 $a(OCoLC)ocn501325397
040 $aSTF$cSTF$dBTCTA$dYDXCP$dOHX$dUBY$dDLC
042 $apcc
050 00 $aQC20.7.D52$bK48 2009
100 1 $aKhalkhali, Masoud,$d1956-
245 10 $aBasic noncommutative geometry /$cMassoud Khakhali.
260 $aZürich :$bEuropean Mathematical Society,$cc2009.
300 $aviii, 223 p. ;$c24 cm.
490 1 $aEMS series of lectures in mathematics
504 $aIncludes bibliographical references (p. [209]-218) and index.
505 0 $aExamples of algebra-geometry correspondences -- Noncommutative quotients -- Cyclic cohomology -- Connes-Chern character -- Appendices: Gelfand-Naimark theorems -- Compact operators, Fredholm operators, and abstract index theory -- Projective modules -- Equivalence of categories.
520 $a"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.
650 0 $aNoncommutative differential geometry.
830 0 $aEMS series of lectures in mathematics.