03086nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100003200199245009500231260008200326300003400408336002600442337002600468338003600494347002400530490006100554506006600615520187300681650004502554650004802599856003202647856006902679109-131128CH-001817-320131128234500.0a fot ||| 0|cr nn mmmmamaa131128e20131213sz fot ||| 0|eng d a978303719628170a10.4171/1282doi ach0018173 7aPBK2bicssc a58-xx2msc1 aKhalkhali, Masoud,eauthor.10aBasic Noncommutative Geometryh[electronic resource] :bSecond edition /cMasoud Khalkhali3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (257 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis text provides an introduction to noncommutative geometry and some of its applications. It can be used either as a textbook for a graduate course 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 Connesâ€“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. Two new sections have been added to this second edition: one concerns the Gaussâ€“Bonnet theorem and the definition and computation of the scalar curvature of the curved noncommutative two torus, and the second is a brief introduction to Hopf cyclic cohomology. The bibliography has been extended and some new examples are presented.07aCalculus & mathematical analysis2bicssc07aGlobal analysis, analysis on manifolds2msc40uhttps://doi.org/10.4171/128423cover imageuhttps://www.ems-ph.org/img/books/khalkhali_mini.jpg