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008			081109s1994 caua |b 001 0 eng d
020			_a012185860X (acidfree paper)
039		9	_a202302121450 _bshakra _c201402040100 _dVLOAD _c201010021039 _dmalmash _c200811111222 _dvenkatrajand _y200811091432 _zNoora
050	0	0	_aQA564 _b.C6713 1994
100	1		_aConnes, Alain. _925108
240	1	0	_aGeometrie Non Commutative. _lEnglish
245	1	0	_aNoncommutative Geometry / _cAlain Connes.
260			_aSan Diego : _bAcademic Press, _cc1994.
300			_axiii, 661 p. : _bill. ; _c27 cm.
504			_aIncludes bibliographical references (p. 613-644) and index.
505			_aNoncommutative Spaces and Measure Theory: Heisenberg and the Noncommutative Algebra of Physical Quantities Associated to a Microscopic System. Statistical State of a Macroscopic System and Quantum Statistical Mechanics. Modular Theory and the Classification of Factors. Geometric Examples of von Neumann Algebras: Measure Theory of Noncommutative Spaces. The Index Theorem for Measured Foliations. Topology and K-Theory: C*-Algebras and their K-Theory. Elementary Examples of Quotient Spaces. The Space X of Penrose Tilings. Duals of Discrete Groups and the Novikov Conjecture. The Tangent Groupoid of a Manifold. Wrong-way Functionality in K-Theory as a Deformation. The Orbit Space of a GroupAction. The Leaf Space of a Foliation. The Longitudinal Index Theorem for Foliations. The Analytic Assembly Map and Lie Groups. Cyclic Cohomology and Differential Geometry: Cyclic Cohomology. Examples. Pairing of Cyclic Cohomology with K-Theory. The Higher Index Theorem for Covering Spaces. The Novikov Conjecture for Hyperbolic Groups. Factors of Type III, Cyclic Cohomology and the Godbillon-Vey Invariant. The Transverse Fundamental Class for Foliations and Geometric Corollaries. QuantizedCalculus: Quantized Differential Calculus and Cyclic Cohomology. The Dixmier Trace and the Hochschild Class of the Character. Quantized Calculus in One Variable and Fractal Sets. Conformal Manifolds. Fredholm Modules and Rank-One Discrete Groups. Elliptic Theory on the Noncommutative Torus (NOTE: See book for proper symbol. Math T with a 2 over () and the Quantum Hall Effect. Entire Cyclic Cohomology. The Chern Character of (-Summable Fredholm Modules. (-Summable K-Cycles, Discrete Groups, and Quantum Field Theory. Operator Algebras: The Papers of Murray and von Neumann. Representations of C*-Algebras. The Algebraic Framework for Noncommutative Integration and the Theory of Weights. The Factors of Powers, Araki and Woods,and of Krieger. The Radon-Nikodom Theorem and Factors of Type III(. Noncommutati
520			_aThis English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields. It includes features such as: first full treatment of the subject and its applications; written by the pioneer of this field; broad applications in mathematics; of interest across most fields; ideal as an introduction and survey; examples treated include: @subbul; the space of Penrose tilings; the space of leaves of a foliation; the space of irreducible unitary representations of a discrete group; the phase space in quantum mechanics; the Brillouin zone in the quantum Hall effect; and a model of space time.
650		0	_aGeometry, Algebraic. _910151
942			_2lcc _n0 _cBK
999			_c10347 _d10347