Introduction to Topological Manifolds

  • John M. Lee

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

  • John M. Lee
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7940-7
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7939-1
  • Online ISBN 978-1-4419-7940-7
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • About this book