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Singularities of Mappings

The Local Behaviour of Smooth and Complex Analytic Mappings

  • David Mond
  • Juan J. Nuño-Ballesteros
Book

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 357)

Table of contents

  1. Front Matter
    Pages i-xv
  2. David Mond, Juan J. Nuño-Ballesteros
    Pages 1-10
  3. Thom-Mather Theory: Right-Left Equivalence, Stability, Versal Unfoldings, Finite Determinacy

    1. Front Matter
      Pages 11-11
    2. David Mond, Juan J. Nuño-Ballesteros
      Pages 13-44
    3. David Mond, Juan J. Nuño-Ballesteros
      Pages 45-96
    4. David Mond, Juan J. Nuño-Ballesteros
      Pages 97-139
    5. David Mond, Juan J. Nuño-Ballesteros
      Pages 141-179
    6. David Mond, Juan J. Nuño-Ballesteros
      Pages 181-216
    7. David Mond, Juan J. Nuño-Ballesteros
      Pages 217-250
  4. Images and Discriminants: The Topology of Stable Perturbations

    1. Front Matter
      Pages 251-251
    2. David Mond, Juan J. Nuño-Ballesteros
      Pages 253-301
    3. David Mond, Juan J. Nuño-Ballesteros
      Pages 303-368
    4. David Mond, Juan J. Nuño-Ballesteros
      Pages 369-412
    5. David Mond, Juan J. Nuño-Ballesteros
      Pages 413-468
  5. Back Matter
    Pages 469-567

About this book

Introduction

The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings.

Part I of the book develops the now classical real C and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic.

By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.

Keywords

singularity theory Multiplicity Milnor-Tjurina relation vanishing homology left-right equivalence Finite determinancy Image and discriminant Multiple point spaces

Authors and affiliations

  • David Mond
    • 1
  • Juan J. Nuño-Ballesteros
    • 2
  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Departament de MatemàtiquesUniversitat de ValènciaBurjassotSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-34440-5
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-34439-9
  • Online ISBN 978-3-030-34440-5
  • Series Print ISSN 0072-7830
  • Series Online ISSN 2196-9701
  • Buy this book on publisher's site