000			02388 a2200301 4500
003			OSt
005			20250217140913.0
008			241016b |||||||| |||| 00| 0 eng d
020			_a9781489994752 (pbk.) _c€ 49.99
040			_cIISER-BPR
041			_aENG
082			_a516.362 _bLEE _223rd
100			_aLee, John M. _9252
222			_aMathematics
245			_aIntroduction to smooth manifolds
250			_a2nd ed.
260			_aNew York: _bSpringer, _cc2012.
300			_axv, 708p. : _bill. ; _c24cm.
440			_aGraduate Texts in Mathematics _vVol. 218 _9253
504			_aIncludes illustrations, appendices, notation index and 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 fewnew 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			_aMathematics _9254
650			_aGeometry _92973
650			_aAnalytic Geometries _9255
650			_aIntegral Geometry _9256
650			_aSmooth Manifolds _9257
942			_2ddc _cBK _02
999			_c4194 _d4194