Stratified Morse Theory
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....
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1988, 1988
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| Edition: | 1st ed. 1988 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Stratified Morse Theory
- 2. The Topology of Complex Analytic Varieties and the Lefschetz Hyperplane Theorem
- I. Morse Theory of Whitney Stratified Spaces
- 1. Whitney Stratifications and Subanalytic Sets
- 2. Morse Functions and Nondepraved Critical Points
- 3. Dramatis Personae and the Main Theorem
- 4. Moving the Wall
- 5. Fringed Sets
- 6. Absence of Characteristic Covectors: Lemmas for Moving the Wall
- 7. Local, Normal, and Tangential Morse Data are Well Defined
- 8. Proof of the Main Theorem
- 9. Relative Morse Theory
- 10. Nonproper Morse Functions
- 11. Relative Morse Theory of Nonproper Functions
- 12. Normal Morse Data of Two Morse Functions
- II. Morse Theory of Complex Analytic Varieties
- 0. Introduction
- 1. Statement of Results
- 2. Normal Morse Data for Complex Analytic Varieties
- 3. Homotopy Type of the Morse Data
- 4. Morse Theory of the Complex Link
- 5. Proof of the Main Theorems
- 6. Morse Theory and Intersection Homology
- 7. Connectivity Theorems for q-Defective Pairs
- 8. Counterexamples
- III. Complements of Affine Subspaces
- 0. Introduction
- 1. Statement of Results
- 2. Geometry of the Order Complex
- 3. Morse Theory of ?n
- 4. Proofs of Theorems B, C, and D
- 5. Examples