Introduction to Smooth Manifolds

  • John M. Lee

Part of the Graduate Texts in Mathematics book series (GTM, volume 218)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. John M. Lee
    Pages 1-29
  3. John M. Lee
    Pages 30-59
  4. John M. Lee
    Pages 60-79
  5. John M. Lee
    Pages 80-102
  6. John M. Lee
    Pages 103-123
  7. John M. Lee
    Pages 124-154
  8. John M. Lee
    Pages 155-172
  9. John M. Lee
    Pages 173-205
  10. John M. Lee
    Pages 206-240
  11. John M. Lee
    Pages 241-259
  12. John M. Lee
    Pages 260-290
  13. John M. Lee
    Pages 291-323
  14. John M. Lee
    Pages 324-348
  15. John M. Lee
    Pages 349-387
  16. John M. Lee
    Pages 388-409
  17. John M. Lee
    Pages 410-433
  18. John M. Lee
    Pages 434-463
  19. John M. Lee
    Pages 464-493
  20. John M. Lee
    Pages 494-517

About this book

Introduction

Manifolds are everywhere. These generalizations of curves and surfaces to arbitrarily many dimensions provide the mathematical context for under­ standing "space" in all of its manifestations. Today, the tools of manifold theory are indispensable in most major subfields of pure mathematics, and outside of pure mathematics they are becoming increasingly important to scientists in such diverse fields as genetics, robotics, econometrics, com­ puter graphics, biomedical imaging, and, of course, the undisputed leader among consumers (and inspirers) of mathematics-theoretical physics. No longer a specialized subject that is studied only by differential geometers, manifold theory is now one of the basic skills that all mathematics students should acquire as early as possible. Over the past few centuries, mathematicians have developed a wondrous collection of conceptual machines designed to enable us to peer ever more deeply into the invisible world of geometry in higher dimensions. Once their operation is mastered, these powerful machines enable us to think geometrically about the 6-dimensional zero set of a polynomial in four complex variables, or the lO-dimensional manifold of 5 x 5 orthogonal ma­ trices, as easily as we think about the familiar 2-dimensional sphere in ]R3.

Keywords

Algebra Cohomology De Rham cohomology Fundamental group foliation homology vector bundle

Authors and affiliations

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-21752-9
  • Copyright Information Springer Science+Business Media New York 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-95448-6
  • Online ISBN 978-0-387-21752-9
  • Series Print ISSN 0072-5285
  • About this book