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  • Textbook
  • © 2011

Introduction to Topological Manifolds

Authors:

  • 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

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

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eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4419-7940-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 74.95
Price excludes VAT (USA)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xvii
  2. Introduction

    • John M. Lee
    Pages 1-17
  3. Topological Spaces

    • John M. Lee
    Pages 19-48
  4. New Spaces from Old

    • John M. Lee
    Pages 49-84
  5. Connectedness and Compactness

    • John M. Lee
    Pages 85-126
  6. Cell Complexes

    • John M. Lee
    Pages 127-158
  7. Compact Surfaces

    • John M. Lee
    Pages 159-182
  8. Homotopy and the Fundamental Group

    • John M. Lee
    Pages 183-216
  9. The Circle

    • John M. Lee
    Pages 217-231
  10. Some Group Theory

    • John M. Lee
    Pages 233-250
  11. The Seifert–Van Kampen Theorem

    • John M. Lee
    Pages 251-275
  12. Covering Maps

    • John M. Lee
    Pages 277-305
  13. Group Actions and Covering Maps

    • John M. Lee
    Pages 307-337
  14. Homology

    • John M. Lee
    Pages 339-380
  15. Back Matter

    Pages 381-433

About this book

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

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)

  

Authors and Affiliations

  • Department of Mathematics, University of Washington, Seattle, USA

    John M. Lee

About the author

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

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4419-7940-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 74.95
Price excludes VAT (USA)