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Stratified Morse Theory

  • Mark Goresky
  • Robert MacPherson

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 14)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Mark Goresky, Robert MacPherson
      Pages 3-22
  3. Morse Theory of Whitney Stratified Spaces

    1. Front Matter
      Pages 31-31
    2. Mark Goresky, Robert MacPherson
      Pages 33-49
    3. Mark Goresky, Robert MacPherson
      Pages 50-59
    4. Mark Goresky, Robert MacPherson
      Pages 60-69
    5. Mark Goresky, Robert MacPherson
      Pages 70-76
    6. Mark Goresky, Robert MacPherson
      Pages 77-80
    7. Mark Goresky, Robert MacPherson
      Pages 81-89
    8. Mark Goresky, Robert MacPherson
      Pages 90-99
    9. Mark Goresky, Robert MacPherson
      Pages 100-113
    10. Mark Goresky, Robert MacPherson
      Pages 114-118
    11. Mark Goresky, Robert MacPherson
      Pages 119-123
    12. Mark Goresky, Robert MacPherson
      Pages 124-127
    13. Mark Goresky, Robert MacPherson
      Pages 128-143
  4. Morse Theory of Complex Analytic Varieties

    1. Front Matter
      Pages 145-145
    2. Mark Goresky, Robert MacPherson
      Pages 147-149
    3. Mark Goresky, Robert MacPherson
      Pages 150-158
    4. Mark Goresky, Robert MacPherson
      Pages 159-172
    5. Mark Goresky, Robert MacPherson
      Pages 173-175
    6. Mark Goresky, Robert MacPherson
      Pages 176-194
    7. Mark Goresky, Robert MacPherson
      Pages 195-207
    8. Mark Goresky, Robert MacPherson
      Pages 208-224
    9. Mark Goresky, Robert MacPherson
      Pages 225-229
    10. Mark Goresky, Robert MacPherson
      Pages 230-231
  5. Complements of Affine Subspaces

    1. Front Matter
      Pages 233-233
    2. Mark Goresky, Robert MacPherson
      Pages 235-236
    3. Mark Goresky, Robert MacPherson
      Pages 237-240
    4. Mark Goresky, Robert MacPherson
      Pages 241-244
    5. Mark Goresky, Robert MacPherson
      Pages 245-250
    6. Mark Goresky, Robert MacPherson
      Pages 251-255
    7. Mark Goresky, Robert MacPherson
      Pages 256-257
  6. Back Matter
    Pages 258-274

About this book

Introduction

Due to the lack of proper bibliographical sources stratification theory seems to be a "mysterious" subject in contemporary mathematics. This book contains a complete and elementary survey - including an extended bibliography - on stratification theory, including its historical development. Some further important topics in the book are: Morse theory, singularities, transversality theory, complex analytic varieties, Lefschetz theorems, connectivity theorems, intersection homology, complements of affine subspaces and combinatorics. The book is designed for all interested students or professionals in this area.

Keywords

Area Dimension Homotopy Levi form Submersion boundary element method character function geometry homology manifold mathematics proof sheaves topology

Authors and affiliations

  • Mark Goresky
    • 1
  • Robert MacPherson
    • 2
  1. 1.Department of MathematicsNortheastern UniversityBostonUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-71714-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-71716-1
  • Online ISBN 978-3-642-71714-7
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site