An introduction to manifolds / Loring W. Tu.

By:

Tu, Loring W

Material type: Text

TextSeries: UniversitextPublication details: New York : Springer, c2011.Edition: 2nd edDescription: xviii, 410 p. : ill. ; 23 cmISBN:

9781441973993 (acidfree paper)
9781441974006 (ebook)

Subject(s):

Manifolds (Mathematics)

DDC classification:

516.07 23 TU

LOC classification:

QA613 .T8 2011

Contents:

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

Summary: 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'.

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Holdings
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

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'.

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