Editorial Reviews. Review. From the reviews: “An introduction to the formalism of differential and integral calculus on smooth manifolds. Many prospective. Loring W. Tu. An Introduction to Manifolds. Second Edition. May 19, Springer. Berlin Heidelberg NewYork. HongKong London. Loring W. Tu Tu’s An Introduction to Manifolds is accordingly offered as the first of a quartet of works that should make for a fine education in.
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Combining aspects of algebra, topology, and analysis, manifolds mznifolds also been applied to classical mechanics, general relativity, and quantum field lring. 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. The Best Books of Check out the top books of the year on our page Best Books of Product details Format Paperback pages Dimensions x x Looking for beautiful books?
Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Other books in this series. An Introduction to Manifolds Loring W. Ordinary Differential Equations Vladimir I. Probability Essentials Jean Jacod.
reference request – Introductory texts on manifolds – Mathematics Stack Exchange
Differential Forms and Applications Manfredo P. Mathematical Analysis I Vladimir A. Number Fields Daniel A. Probability Inttroduction Achim Klenke. Complex Geometry Daniel Huybrechts.
Lie Groups Claudio Procesi. The Calculus of Variations Bruce van Brunt. Spectra of Graphs Andries E. Logic and Structure Dirk Van Dalen. Riemannian Geometry Sylvestre Gallot. Back cover copy Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics.
Along the way the reader acquires the tp and skills necessary for further study of geometry and topology. The second edition contains fifty pages of new material.
Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study.
The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra.
An Introduction to Manifolds
Requiring only minimal undergraduate prerequisites, “An Introduction to Manifolds” is also an excellent foundation for the author’s publication with Raoul Bott, “Differential Forms in Algebraic Topology.
Table of contents Preface to the Second Edition. Smooth Functions ontroduction a Euclidean Space. Tangent Vectors in R N as Derivativations. The Exterior Algebra of Multicovectors.
Differential Forms on R N. Smooth Maps on a Manifold.
The Tl of a Smooth Map. Bump Functions and Partitions of Unity. Lie Groups and Lie Algebras. The Lie Derivative and Interior Multiplication. The Long Exact Sequence in Cohomology. The Mayer -Vietoris Sequence. Computation of de Rham Cohomology. Proof of Homotopy Invariance.
Existence of a Partition of Unity in General. Quaternions and the Symplectic Group. Review Text From the reviews of the second edition: Bott and the author.
Assuming only basic background in analysis and algebra, the book offers a rather gentle introduction to smooth manifolds and differential forms offering the necessary background to understand and compute deRham cohomology. The text also contains many exercises Review quote From the reviews of the second edition: Cap, Monatshefte fur Mathematik, Vol. An algebraic geometer by training, he has done research at the interface of algebraic geometry,topology, and differential geometry, including Hodge theory, degeneracy loci, moduli spaces of vector bundles, and equivariant cohomology.
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