Advertisement

© 2011

Introduction to Topological Manifolds

Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 202)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. John M. Lee
    Pages 1-17
  3. John M. Lee
    Pages 19-48
  4. John M. Lee
    Pages 49-84
  5. John M. Lee
    Pages 85-126
  6. John M. Lee
    Pages 127-158
  7. John M. Lee
    Pages 159-182
  8. John M. Lee
    Pages 183-216
  9. John M. Lee
    Pages 217-231
  10. John M. Lee
    Pages 233-250
  11. John M. Lee
    Pages 251-275
  12. John M. Lee
    Pages 277-305
  13. John M. Lee
    Pages 307-337
  14. John M. Lee
    Pages 339-380
  15. Back Matter
    Pages 381-433

About this book

Introduction

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.

Keywords

Cell complexes Covering spaces Homology Surfaces The fundamental group Topological spaces Topology

Authors and affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

About the authors

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.

Bibliographic information

Reviews

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)