Graduate Texts in Mathematics

Introduction to Topological Manifolds

Authors: Lee, John

  • New edition extensively revised and updated
  • New introduction to CW complexes (along with a brief and streamlined introduction to simplicial complexes)
  • Expanded treatments of manifolds with boundary, local compactness, group actions, proper maps, and a new section on paracompactness
see more benefits

Buy this book

eBook $54.99
price for USA
  • ISBN 978-1-4419-7940-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Hardcover $74.95
price for USA
  • ISBN 978-1-4419-7939-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-1-4614-2790-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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.

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.

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)


  

Table of contents (13 chapters)

Buy this book

eBook $54.99
price for USA
  • ISBN 978-1-4419-7940-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Hardcover $74.95
price for USA
  • ISBN 978-1-4419-7939-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-1-4614-2790-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Bibliographic Information

Bibliographic Information
Book Title
Introduction to Topological Manifolds
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
940
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-7940-7
DOI
10.1007/978-1-4419-7940-7
Hardcover ISBN
978-1-4419-7939-1
Softcover ISBN
978-1-4614-2790-2
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XVII, 433
Topics