000			03785nam a22004575i 4500
003			DE-He213
005			20191011041631.0
007			cr nn 008mamaa
008			120824s2012 xxu| s |||| 0|eng d
020	6	4	_a9781441999825 _9978-1-4419-9982-5
024	8	7	_a10.1007/978-1-4419-9982-5 _2doi
050	8	4	_aQA641-670
072	8	7	_aPBMP _2bicssc
072	8	7	_aMAT012030 _2bisacsh
082			_a516.36 _223
100	8	1	_aLee, John M. _eauthor. _967059
245	9	7	_aIntroduction to Smooth Manifolds _h[electronic resource] / _cby John M. Lee.
001			000053692
250	6	4	_a2nd ed. 2012.
300	6	4	_aXVI, 708 p. _bonline resource.
490	8	1	_aGraduate Texts in Mathematics, _x0072-5285 ; _v218
505	8	0	_aPreface -- 1 Smooth Manifolds -- 2 Smooth Maps -- 3 Tangent Vectors -- 4 Submersions, Immersions, and Embeddings -- 5 Submanifolds -- 6 Sard's Theorem -- 7 Lie Groups -- 8 Vector Fields -- 9 Integral Curves and Flows -- 10 Vector Bundles -- 11 The Cotangent Bundle -- 12 Tensors -- 13 Riemannian Metrics -- 14 Differential Forms -- 15 Orientations -- 16 Integration on Manifolds.-17 De Rham Cohomology.-18 The de Rham Theorem -- 19Distributions and Foliations.-20 The Exponential Map.-21 Quotient Manifolds.- 22 Symplectic Manifolds -- Appendix A: Review of Topology -- Appendix B: Review of Linear Algebra -- Appendix C: Review of Calculus -- Appendix D: Review of Differential Equations -- References -- Notation Index -- Subject Index.
520	6	4	_aThis book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific researchsmooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sards theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
650	8	0	_aMathematics. _98571
650	8	0	_aGlobal differential geometry. _99530
650			_aMathematics. _98571
650			_aDifferential Geometry. _99532
710	8	2	_aSpringerLink (Online service) _967060
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9781441999818
830	8	0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v218 _967061
856			_uhttp://dx.doi.org/10.1007/978-1-4419-9982-5 _zde clik aquí para ver el libro electrónico
264	8	1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2012.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
516	6	4	_aZDB-2-SMA
999			_c53422 _d53422
942			_c05