Stable Mappings and Their Singularities

  • Martin Golubitsky
  • Victor Guillemin

Part of the Graduate Texts in Mathematics book series (GTM, volume 14)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Martin Golubitsky, Victor Guillemin
    Pages 1-29
  3. Martin Golubitsky, Victor Guillemin
    Pages 30-71
  4. Martin Golubitsky, Victor Guillemin
    Pages 72-90
  5. Martin Golubitsky, Victor Guillemin
    Pages 91-110
  6. Martin Golubitsky, Victor Guillemin
    Pages 111-142
  7. Martin Golubitsky, Victor Guillemin
    Pages 143-164
  8. Martin Golubitsky, Victor Guillemin
    Pages 165-193
  9. Back Matter
    Pages 194-209

About this book

Introduction

This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu­ larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather.

Keywords

Immersion Mappings Submersion Umbilical point manifold

Authors and affiliations

  • Martin Golubitsky
    • 1
  • Victor Guillemin
    • 2
  1. 1.Department of MathematicsQueens CollegeFlushingUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-7904-5
  • Copyright Information Springer-Verlag New York 1973
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90073-5
  • Online ISBN 978-1-4615-7904-5
  • Series Print ISSN 0072-5285
  • About this book