Introduction to Topological Manifolds

John Lee

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English

Springer-Verlag New York Inc.
30 December 2010

Mathematics & Sciences; Topology; Algebraic topology

Series: Graduate Texts in Mathematics

This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition.

Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.

This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author’s book Introduction to Smooth Manifolds is meant to act as a sequel to this book.

By: John Lee
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: 2nd ed. 2011
Volume: 202
Dimensions: Height: 235mm, Width: 155mm, Spine: 25mm
Weight: 1.780kg
ISBN: 9781441979391
ISBN 10: 1441979395
Series: Graduate Texts in Mathematics
Pages: 452
Publication Date: 30 December 2010
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

John M. Lee is a professor of mathematics at the University of Washington. His previous Springer textbooks in the Graduate Texts in Mathematics series include the first edition of Introduction to Topological Manifolds, Introduction to Smooth Manifolds, and Riemannian Manifolds: An Introduction.

Reviews for Introduction to Topological Manifolds

From the reviews of the second edition: An excellent introduction to both point-set and algebraic topology at the early-graduate level, using manifolds as a primary source of examples and motivation. ... The author has ... fulfilled his objective of integrating a study of manifolds into an introductory course in general and algebraic topology. This text is well-organized and clearly written, with a good blend of motivational discussion and mathematical rigor. ... Any student who has gone through this book should be well-prepared to pursue the study of differential geometry ... . (Mark Hunacek, The Mathematical Association of America, March, 2011) This book is designed for first year graduate students as an introduction to the topology of manifolds. ... The book can be read with advantage by any graduate student with a good undergraduate background, and indeed by many upper class undergraduates. It can be used for self study or as a text book for a fine geometrically flavored introduction to manifolds. One which provides excellent motivation for studying the machinery needed for more advanced work. (Jonathan Hodgson, Zentralblatt MATH, Vol. 1209, 2011)