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Introduction to manifolds

Author: Loring W Tu
Publisher: New York : Springer, ©2008.
Series: Universitext.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
"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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Tu, Loring W.
Introduction to manifolds.
New York : Springer, ©2008
(DLC) 2007932203
(OCoLC)186358733
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Loring W Tu
ISBN: 9780387481012 038748101X 0387480986 9780387480985
OCLC Number: 233971274
Description: 1 online resource (xv, 360 pages) : illustrations.
Contents: 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.
Series Title: Universitext.
Responsibility: Loring W. Tu.

Abstract:

In this streamlined introduction to the subject, the theory of manifolds is presented to help the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be  Read more...

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From the reviews: "An introduction to the formalism of differential and integral calculus on smooth manifolds. ... Many prospective readers of Bott and Tu will welcome this volume. ... Summing Up: Read more...

 
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