000 03713nam a22004455i 4500
001 978-1-4419-9982-5
003 DE-He213
005 20140220083234.0
007 cr nn 008mamaa
008 120824s2012 xxu| s |||| 0|eng d
020 _a9781441999825
_9978-1-4419-9982-5
024 7 _a10.1007/978-1-4419-9982-5
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
082 0 4 _a516.36
_223
100 1 _aLee, John M.
_eauthor.
245 1 0 _aIntroduction to Smooth Manifolds
_h[electronic resource] /
_cby John M. Lee.
250 _a2nd ed. 2012.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2012.
300 _aXV, 708 p. 150 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v218
505 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 -- 19 Distributions 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 _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 research—smooth 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 Sard’s 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 0 _aMathematics.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aDifferential Geometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441999818
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v218
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-9982-5
912 _aZDB-2-SMA
999 _c100612
_d100612