An introduction to manifolds / Loring W. Tu.
Material type: TextSeries: UniversitextPublication details: New York : Springer, c2011.Edition: 2nd edDescription: xviii, 410 p. : ill. ; 23 cmISBN:- 9781441973993 (acidfree paper)
- 9781441974006 (ebook)
- 516.07 23 TU
- QA613 .T8 2011
Item type | Current library | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|
Project book | CUTN Central Library Sciences | Non-fiction | 516.07 TU (Browse shelf(Opens below)) | Checked out to Renuka Devi V (20019T) | 31/01/2024 | 48814 |
Browsing CUTN Central Library shelves, Shelving location: Sciences, Collection: Non-fiction Close shelf browser (Hides shelf browser)
515.984 AND Ramanujan's lost notebook(Part IV) / | 516.04 KUM A First Course in Ordinary Differential Equations / | 516.04 MUN Analysis on Manifolds / | 516.07 TU An introduction to manifolds / | 516.08 SOL Lectures on convex sets / | 516.244 WHI Spherical Geometry and Its Applications / | 516.35 BUM Algebraic geometry / |
Includes bibliographical references (p. [395]-396) and index.
A Brief Introduction
Loring W. Tu
Pages 1-2
Euclidean Spaces
Loring W. Tu
Pages 3-45
Manifolds
Loring W. Tu
Pages 47-83
The Tangent Space
Loring W. Tu
Pages 85-162
Lie Groups and Lie Algebras
Loring W. Tu
Pages 163-188
Differential Forms
Loring W. Tu
Pages 189-234
Integration
Loring W. Tu
Pages 235-272
De Rham Theory
Loring W. Tu
Pages 273-316
Back Matter
Pages 317-410
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, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
There are no comments on this title.