000			02153nam a2200313Ia 4500
003			OSt
005			20250325020504.0
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020			_a9781441973993 (pbk.) _c€ 49.99
040			_bENG _cIISER-BPR
041			_aENG
082			_a516.07 _bLOR _223rd
100			_aLoring W. Tu _91063
222			_aMatrhematics
245		3	_aAn introduction to manifolds
250			_a2nd ed.
260			_aNew York: _bSpringer Science, _cc2011
300			_axviii, 410p. : _bill. ; _c24cm
440			_aUniversitext _92577
504			_aIncludes illustrations, appendices, list of notation, bibliographic references and subject index.
520			_aManifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
650			_aMathematics _92578
650			_aGeometry _92579
650			_aManifolds _92580
942			_cBK _2ddc _04
942			_2ddc
947			_a4581.583500000001
948			_a22
999			_c4203 _d4203