000			03268nam a22003855a 4500
001			109-131128
003			CH-001817-3
005			20170613140752.0
006			a fot ||| 0|
007			cr nn mmmmamaa
008			131128e20131213sz fot ||| 0|eng d
020			_a9783037196281
024	7	0	_a10.4171/128 _2doi
040			_ach0018173
072		7	_aPBK _2bicssc
084			_a58-xx _2msc
100	1		_aKhalkhali, Masoud, _eauthor.
245	1	0	_aBasic Noncommutative Geometry _h[electronic resource] : _bSecond edition / _cMasoud Khalkhali
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2013
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2013
300			_a1 online resource (257 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aEMS Series of Lectures in Mathematics (ELM)
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
520			_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 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. Two new sections have been added to this second edition: one concerns the Gauss–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.
650	0	7	_aCalculus & mathematical analysis _2bicssc
650	0	7	_aGlobal analysis, analysis on manifolds _2msc
700	1		_aKhalkhali, Masoud, _eauthor.
856	4	0	_uhttps://doi.org/10.4171/128
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/khalkhali_mini.jpg
942			_2EBK13787 _cEBK
999			_c50411 _d50411