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Field name	Details
Dewey Class	516.36
Title	Introduction to Smooth Manifolds ([EBook]) / by John M. Lee.
Author	Lee, John M. , 1950-
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 2003.
Physical Details	XVII, 631 pages, 63 illus. : online resource.
Series	Graduate texts in mathematics 0072-5285 ; ; 218
ISBN	9780387217529
Summary Note	Manifolds are everywhere. These generalizations of curves and surfaces to arbitrarily many dimensions provide the mathematical context for under standing "space" in all of its manifestations. Today, the tools of manifold theory are indispensable in most major subfields of pure mathematics, and outside of pure mathematics they are becoming increasingly important to scientists in such diverse fields as genetics, robotics, econometrics, com puter graphics, biomedical imaging, and, of course, the undisputed leader among consumers (and inspirers) of mathematics-theoretical physics. No longer a specialized subject that is studied only by differential geometers, manifold theory is now one of the basic skills that all mathematics students should acquire as early as possible. Over the past few centuries, mathematicians have developed a wondrous collection of conceptual machines designed to enable us to peer ever more deeply into the invisible world of geometry in higher dimensions. Once their operation is mastered, these powerful machines enable us to think geometrically about the 6-dimensional zero set of a polynomial in four complex variables, or the lO-dimensional manifold of 5 x 5 orthogonal ma trices, as easily as we think about the familiar 2-dimensional sphere in ]R3.:
Contents note	1 Smooth Manifolds -- 2 Smooth Maps -- 3 Tangent Vectors -- 4 Vector Fields -- 5 Vector Bundles -- 6 The Cotangent Bundle -- 7 Submersions, Immersions, and Embeddings -- 8 Submanifolds -- 9 Lie Group Actions -- 10 Embedding and Approximation Theorems -- 11 Tensors -- 12 Differential Forms -- 13 Orientations -- 14 Integration on Manifolds -- 15 De Rham Cohomology -- 16 The de Rham Theorem -- 17 Integral Curves and Flows -- 18 Lie Derivatives -- 19 Integral Manifolds and Foliations -- 20 Lie Groups and Their Lie Algebras -- Appendix: Review of Prerequisites -- Topology -- Linear Algebra -- Calculus -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-387-21752-9
Links to Related Works	Subject References: Complex manifolds . Differential Geometry . Manifolds and Cell Complexes (incl. Diff.Topology) . Manifolds (Mathematics) . Mathematics . Topology . Authors: Lee, John M. 1950- . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 516.36 . 516.36 (DDC 23) .

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Introduction to Smooth Manifolds

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