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Field name	Details
Dewey Class	514.34
Title	An Introduction to Manifolds ([Ebook]) / by Loring W. Tu.
Author	Tu, Loring W.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 2008.
Physical Details	XVI, 368 pages, 104 illus. : online resource.
Series	Universitext
ISBN	9780387481012
Summary Note	Manifolds, 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, An Introduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology.:
Contents note	A Brief Introduction -- Part I. The Euclidean Space -- Smooth Functions on R(N) -- Tangent Vectors In R(N) as Derivations -- Alternating K-Linear Functions -- Differential Forms on R(N) -- Part II. Manifolds -- Manifolds -- Smooth Maps on A Manifold -- Quotient -- Part III. The Tangent Space -- The Tangent Space -- Submanifolds -- Categories And Functors -- The Image of A Smooth Map -- The Tangent Bundle -- Bump Functions and Partitions of Unity -- Vector Fields -- Part IV. Lie Groups and Lie Algebras -- Lie Groups -- Lie Algebras -- Part V. Differential Forms -- Differential 1-Forms -- Differential K-Forms -- The Exterior Derivative -- Part VI. Integration -- Orientations -- Manifolds With Boundary -- Integration on A Manifold -- Part VII. De Rham Theory -- De Rham Cohomology -- The Long Exact Sequence in Cohomology -- The Mayer-Vietoris Sequence -- Homotopy Invariance -- Computation of De Rham Cohomology -- Proof of Homotopy Invariance -- Appendix A. Point-Set Topology -- Appendix B. Inverse Function Theorem of R(N) And Related Results -- Appendix C. Existence of A Partition of Unity in General -- Appendix D. Solutions to Selected Exercises -- Bibliography -- Index.
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/10.1007/978-0-387-48101-2
Links to Related Works	Subject References: Cell aggregation . Differential Geometry . Global analysis . Global Analysis and Analysis on Manifolds . Global differential geometry . Manifolds and Cell Complexes (incl. Diff.Topology) . Manifolds (Mathematics) . Mathematics . Authors: Tu, Loring W. . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 514.34 . 514.34 (DDC 22) .

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An Introduction to Manifolds

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