Critical Point Theory in Global Analysis and Differential Topology

Name: Critical Point Theory in Global Analysis and Differential Topology | An introduction
Brand: Academic Press
Price: 54.95 EUR
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An introduction

Academic Press

Erschienen am 1. Januar 1969

388 Seiten

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978-0-08-087345-9 (ISBN)

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Front Cover
Critical Point Theory in Global Analysis and Differential Topology: An Introduction
Copyright Page
Contents
Preface
Introduction
Part I: Analysis of Nondegenerate Functions
Chapter 1. Differentiable Mappings
Chapter 2. Laws of the Mean
Chapter 3. Real, Symmetric, Quadratic Forms
Chapter 4. The Reduction Theorem for ƒ
Chapter 5. Regular Manifolds in Euclidean Spaces
Chapter 6. First Theorems on Nondegeneracy
Chapter 7. Nondegeneracy: Theorem 7.1
Chapter 8. S-Normal f-Coordinates
Chapter 9. Nondegenerate Functions under Boundary Conditions A
Chapter 10. Nondegenerate Functions under Boundary Conditions B
Chapter 11. Proof of Theorem 10.1 under Boundary Conditions B
Chapter 12. ƒ-level Boundaries
Part II : Abstract Differentiable Manifolds
Chapter 13. The Manifolds Defined
Chapter 14. Families of Differentiable Functions on Mn
Chapter 15. Focal Points of Regular Manifolds
Chapter 16. Differentiable Mappings of Manifolds into Manifolds
Chapter 17. Dynamical Systems on a Manifold Mn
Chapter 18. Tangent and Cotangent Vectors of Mn
Chapter 19. Mn As Riemannian Manifold
Chapter 20. ƒƒ-Presentations in DMnƒ
Chapter 21, ƒ-Trajectories on Mnf
Chapter 22. ƒ-Preferred Riemannian Structures S´
Chapter 23. The Basic Homotopy Theorem
Part III : Singular Homology Theory
Chapter 24. Introduction
Chapter 25. Model Polyhedral Complexes P
Chapter 26. Singular Complexes S(x). Eilenberg
Chapter 27. Chain-Homotopies on S(x)
Chapter 28. Relative Homologies
Chapter 29. Comparison of the Homology Groups on fa and on fa - pa
Chapter 30. Type Numbers and Connectivities
Part IV: Other Applications of Critical Point Theory
Chapter 31. Normals from a Point to a Manifold
Chapter 32. Equilibrium Points of an Electrostatic Potential
Chapter 33. Symmetric Squares of Manifolds and Critical Chords
Chapter 34. The Symmetric Square of an n-Sphere
Chapter 35. The Complex Projective n-Space CPn
Chapter 36. Caps and Saddles
Chapter 37. The Real Projective n-Space Pn
Chapter 38. Stein Manifolds. A Theorem of Lefschetz
Chapter 39. Supplementary Concepts and Theorems
Appendix I. Preliminary Definitions
Appendix II. On Elevating Manifold Differentiability
Appendix III. Singular Homology Theory on Mn over Z
Fundamental Symbols
Bibliography
Index of Terms
Pure and Applied Mathematics

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