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Stratified Morse Theory

  • Book
  • © 1988

Overview

Authors:
  1. Mark Goresky

    1. Department of Mathematics, Northeastern University, Boston, USA

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  2. Robert MacPherson

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (29 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. Stratified Morse Theory

      • Mark Goresky, Robert MacPherson
      Pages 3-22

    3. The Topology of Complex Analytic Varieties and the Lefschetz Hyperplane Theorem

      • Mark Goresky, Robert MacPherson
      Pages 23-29

  3. Morse Theory of Whitney Stratified Spaces

    1. Front Matter

      Pages 31-31
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    2. Whitney Stratifications and Subanalytic Sets

      • Mark Goresky, Robert MacPherson
      Pages 33-49

    3. Morse Functions and Nondepraved Critical Points

      • Mark Goresky, Robert MacPherson
      Pages 50-59

    4. Dramatis Personae and the Main Theorem

      • Mark Goresky, Robert MacPherson
      Pages 60-69

    5. Moving the Wall

      • Mark Goresky, Robert MacPherson
      Pages 70-76

    6. Fringed Sets

      • Mark Goresky, Robert MacPherson
      Pages 77-80

    7. Absence of Characteristic Covectors: Lemmas for Moving the Wall

      • Mark Goresky, Robert MacPherson
      Pages 81-89

    8. Local, Normal, and Tangential Morse Data are Well Defined

      • Mark Goresky, Robert MacPherson
      Pages 90-99

    9. Proof of the Main Theorem

      • Mark Goresky, Robert MacPherson
      Pages 100-113

    10. Relative Morse Theory

      • Mark Goresky, Robert MacPherson
      Pages 114-118

    11. Nonproper Morse Functions

      • Mark Goresky, Robert MacPherson
      Pages 119-123

    12. Relative Morse Theory of Nonproper Functions

      • Mark Goresky, Robert MacPherson
      Pages 124-127

    13. Normal Morse Data of Two Morse Functions

      • Mark Goresky, Robert MacPherson
      Pages 128-143

  4. Morse Theory of Complex Analytic Varieties

    1. Front Matter

      Pages 145-145
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    2. Introduction

      • Mark Goresky, Robert MacPherson
      Pages 147-149

    3. Statement of Results

      • Mark Goresky, Robert MacPherson
      Pages 150-158
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Northeastern University, Boston, USA

    Mark Goresky

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Robert MacPherson

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