
Introduction to Topological Manifolds
John M. Lee(Author)
Springer (Publisher)
Published on 25. May 2000
Book
Hardback
XX, 392 pages
978-0-387-98759-0 (ISBN)
Article exhausted; check for reprint
Description
Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Reviews / Votes
"This book is an introduction to manifolds on the beginning graduate level. It provides a readable text allowing every mathematics student to get a good knowledge of manifolds in the same way that most students come to know real numbers, Euclidean spaces, groups, etc. It starts by showing the role manifolds play in nearly every major branch of mathematics. The book has 13 chapters and can be divided into five major sections. The first section, Chapters 2 through 4, is a brief and sufficient introduction to the ideas of general topology: topological spaces, their subspaces, products and quotients, connectedness and compactness. The second section, Chapters 5 and 6, explores in detail the main examples that motivate the rest of the theory: simplicial complexes, 1- and 2-manifolds. It introduces simplicial complexes in both ways---first concretely, in Euclidean space, and then abstractly, as collections of finite vertex sets. Then it gives classification theorems for 1-manifolds and compact surfaces, essentially following the treatment in W. Massey's \ref[ Algebraic topology: an introduction, Reprint of the 1967 edition, Springer, New York, 1977; MR0448331 (56 \#6638)]. The third section (the core of the book), Chapters 7--10, gives a complete treatment of the fundamental group, including a brief introduction to group theory (free products, free groups, presentations of groups, free abelian groups), as well as the statement and proof of the Seifert-Van Kampen theorem. The fourth major section consists of Chapters 11 and 12, on covering spaces, including proofs that every manifold has a universal covering and that the universal covering space covers every other covering space, as well as quotients by free proper actions of discrete groups. The last Chapter 13 covers homology theory, including homotopy invariance and the Mayer-Vietoris theorem. The book gives an ample opportunity to the reader to learn the subject by working out a large number of examples, exercises and problems. The latter are collected at the end of each chapter." (B.N. Apanasov, Mathematical Reviews)More details
Series
Edition
2000
Language
English
Place of publication
NY
United States
Target group
College/higher education
Professional and scholarly
Graduate
Illustrations
194 s/w Abbildungen
194 black & white illustrations
Dimensions
Height: 22.9 cm
Width: 15.2 cm
Thickness: 25 mm
Weight
1660 gr
ISBN-13
978-0-387-98759-0 (9780387987590)
DOI
10.1007/b98853
Schweitzer Classification
Other editions
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Book
12/2010
2nd Edition
Springer
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John M. Lee
Introduction to Topological Manifolds
E-Book
04/2006
1st Edition
Springer
€85.59
Available for download

John M. Lee
Introduction to Topological Manifolds
Book
05/2000
1st Edition
Springer
€85.59
Article exhausted; check for reprint
Content
Topological Spaces.- New Spaces from Old.- Connectedness and Compactness.- Simplicial Complexes.- Curves and Surfaces.- Homotopy and the Fundamental Group.- Circles and Spheres.- Some Group Theory.- The Seifert-Van Kampen Theorem.- Covering Spaces.- Classification of Coverings.- Homology.