دانلود کتاب Morse Theory. (AM-51), Volume 51

فهرست مطالب :

CONTENTS\nPREFACE\nPART I. NON-DEGENERATE SMOOTH FUNCTIONS ON A MANIFOLD\n §1. Introduction\n §2. Definitions and Lemmas\n §3. Homotopy Type in Terms of Critical Values\n §4. Examples\n §5. The Morse Inequalities\n §6. Manifolds in Euclidean Space: The Existence of Non-degenerate Functions\n §7. The Lefschetz Theorem on Hyperplane Sections\nPART II. A RAPID COURSE IN RIEMANNIAN GEOMETRY\n §8. Covariant Differentiation\n §9. The Curvature Tensor\n §10. Geodesics and Completeness\nPART III. THE CALCULUS OF VARIATIONS APPLIED TO GEODESICS\n §11. The Path Space of a Smooth Manifold\n §12. The Energy of a Path\n §13. The Hessian of the Energy Function at a Critical Path\n §14. Jacobi Fields: The Null-space of E**\n §15. The Index Theorem\n §16. A Finite Dimensional Approximation to Ω^c\n §17. The Topology of the Full Path Space\n §18. Existence of Non-conjugate Points\n §19. Some Relations Between Topology and Curvature\nPART IV. APPLICATIONS TO LIE GROUPS AND SYMMETRIC SPACES\n §20. Symmetric Spaces\n §21. Lie Groups as Symmetric Spaces\n §22. Whole Manifolds of Minimal Geodesics\n §23. The Bott Periodicity Theorem for the Unitary Group\n §24. The Periodicity Theorem for the Orthogonal Group\nAPPENDIX. THE HOMOTOPY TYPE OF A MONOTONE UNION