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Morse theory /
One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study,...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, New Jersey :
Princeton University Press,
[1969]
|
| Colección: | Annals of mathematics studies ;
no. 51. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Part I. Non-degenerate smooth functions on a manifold ; Introduction
- Definitions and lemmas
- Homotopy type in terms of critical values
- Examples
- The Morse inequalities
- Manifolds in Euclidean space : the existence of non-degenerate functions
- The Lefschetz theorem on hyperplane sections
- Part II. A rapid course in Riemannian geometry ; Covariant differentiation
- The curvature tensor
- Geodesics and completeness
- Part III. The calculus of variations applied to geodesics ; The path space of a smooth manifold
- The energy of a path
- The Hessian of the energy function at a critical path
- Jacobi fields : the null-space of E [subscript]**
- The Index theorem
- A finite dimensional approximation to [omega][superscript] c
- The topology of the full path space
- Existence of non-conjugate points
- Some relations between topology and curvature
- Part IV. Applications to Lie groups and symmetric spaces ; Symmetric spaces
- Lie groups as symmetric spaces
- Whole manifolds of minimal geodesics
- The Bott periodicity theorem for the unitary group
- The Periodicity theorem for the orthogonal group
- Appendix. The homotopy type of a monotone union.