Differential Topology

  • Morris W. Hirsch

Part of the Graduate Texts in Mathematics book series (GTM, volume 33)

Table of contents

  1. Front Matter
    Pages N2-x
  2. Morris W. Hirsch
    Pages 1-6
  3. Morris W. Hirsch
    Pages 7-33
  4. Morris W. Hirsch
    Pages 34-66
  5. Morris W. Hirsch
    Pages 67-84
  6. Morris W. Hirsch
    Pages 85-119
  7. Morris W. Hirsch
    Pages 142-168
  8. Morris W. Hirsch
    Pages 169-176
  9. Morris W. Hirsch
    Pages 177-187
  10. Morris W. Hirsch
    Pages 188-208
  11. Back Matter
    Pages 209-221

About this book

Introduction

This book presents some of the basic topological ideas used in studying differentiable manifolds and maps. Mathematical prerequisites have been kept to a minimum; the standard course in analysis and general topology is adequate preparation. An appendix briefly summarizes some of the back­ ground material. In order to emphasize the geometrical and intuitive aspects of differen­ tial topology, I have avoided the use of algebraic topology, except in a few isolated places that can easily be skipped. For the same reason I make no use of differential forms or tensors. In my view, advanced algebraic techniques like homology theory are better understood after one has seen several examples of how the raw material of geometry and analysis is distilled down to numerical invariants, such as those developed in this book: the degree of a map, the Euler number of a vector bundle, the genus of a surface, the cobordism class of a manifold, and so forth. With these as motivating examples, the use of homology and homotopy theory in topology should seem quite natural. There are hundreds of exercises, ranging in difficulty from the routine to the unsolved. While these provide examples and further developments of the theory, they are only rarely relied on in the proofs of theorems.

Keywords

Differentialtopologie Immersion differential topology manifold topology

Authors and affiliations

  • Morris W. Hirsch
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9449-5
  • Copyright Information Springer-Verlag New York 1976
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-9451-8
  • Online ISBN 978-1-4684-9449-5
  • Series Print ISSN 0072-5285
  • About this book