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....
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg,
1988.
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| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics ;
14. |
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Contents. Introduction: Stratified Morse Theory. The Topology of Complex Analytic Varieties and the Lefschetz Hyperplane Theorem
- Morse Theory of Whitney Stratified Spaces: Whitney Stratifications and Subanalytic Sets. Morse Functions and Nondepraved Critical Points. Dramatis Personae and the Main Theorem. Moving the Wall. Fringed Sets. Absence of Characteristic Covectors: Lemmas for Moving the Wall. Local, Normal, and Tangential Morse Data are Well Defined. Proof of the Main Theorem. Relative Morse Theory. Nonproper Morse Functions. Relative Morse Theory of Nonproper Functions
- Normal Morse Data of Two Morse Functions
- Morse Theory of Complex Analytic Varieties: Introduction. Statement of Results. Normal Morse Data for Complex Analytic Spaces. Homotopy Type of the Morse Data. Morse Theory of the Complex Link. Proofs of the Main Theorems. Morse Theory and Intersection Homology. Connectivity Theorems for o-Defective Pairs. Counterexamples
- Complementa of Affine Subspaces: Introduction. Statement of Results. Geometry of the Order Complex. Morse Theory of IRn. Proofs of Theorems B, C, and D
- Examples
- Bibliography
- Index.