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. Pages 1-15
  3. Pages 17-38
  4. Pages 39-63
  5. Pages 91-115
  6. Pages 117-146
  7. Pages 179-192
  8. Pages 193-208
  9. Pages 233-256
  10. Pages 291-335
  11. Back Matter
    Pages 337-387

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 di?erential geometry, algebraic topology, and related ?elds. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. Here at the University of Washington, for example, this text is used for the ?rst third of a year-long course on the geometry and topology of manifolds; the remaining two-thirds focuses on smooth manifolds. Therearemanysuperbtextsongeneralandalgebraictopologyavailable. Why add another one to the catalog? The answer lies in my particular visionofgraduateeducation—itismy(admittedlybiased)beliefthatevery serious student of mathematics needs to know manifolds intimately, in the same way that most students come to know the integers, the real numbers, Euclidean spaces, groups, rings, and ?elds. Manifolds play a role in nearly every major branch of mathematics (as I illustrate in Chapter 1), and specialists in many ?elds ?nd themselves using concepts and terminology fromtopologyandmanifoldtheoryonadailybasis. Manifoldsarethuspart of the basic vocabulary of mathematics, and need to be part of the basic graduate education. The ?rst steps must be topological, and are embodied in this book; in most cases, they should be complemented by material on smooth manifolds, vector ?elds, di?erential forms, and the like. (After all, few of the really interesting applications of manifold theory are possible without using tools from calculus.

Keywords

Manifolds Topology Topology Manifolds differential geometry manifold

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/b98853
  • Copyright Information Springer-Verlag New York, Inc. 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98759-0
  • Online ISBN 978-0-387-22727-6
  • Series Print ISSN 0072-5285
  • About this book