An Introduction

Content: 
Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Preface
Pages vii-x

Introduction
Pages 1-4

§1 Differentiable Mappings
Pages 7-9

§2 Laws of the Mean
Pages 10-14

§3 Real, Symmetric, Quadratic Forms
Pages 15-19

§4 The Reduction Theorem for f
Pages 20-28

§5 Regular Manifolds in Euclidean Spaces
Pages 29-38

§6 First Theorems on Nondegeneracy
Pages 39-49

§7 Nondegeneracy: Theorem 7.1
Pages 50-57

§8 Σ-Normal φ-Coordinates
Pages 58-63

§9 Nondegenerate Functions Under Boundary Conditions A
Pages 64-68

§10 Nondegenerate Functions Under Boundary Conditions B
Pages 69-73

§11 Proof of Theorem 10.1 Under Boundary Conditions B
Pages 74-82

§12 f-Level Boundaries
Pages 83-88

§13 The Manifolds Defined
Pages 91-97

§14 Families of Differentiable Functions on Mn
Pages 98-105

§15 Focal Points of Regular Manifolds
Pages 106-110

§16 Differentiable Mappings of Manifolds Into Manifolds
Pages 111-126

§17 Dynamical Systems on a Manifold Mn
Pages 127-135

§18 Tangent and Cotangent Vectors of Mn
Pages 136-142

§19 Mn as Riemannian Manifold
Pages 143-157

§20 ff-Presentations in Mfn
Pages 158-165

§21 f-Trajectories on Mfn
Pages 166-171

§22 f-Preferred Riemannian Structures Sf
Pages 172-183

§23 The Basic Homotopy Theorem
Pages 184-202

§24 Introduction
Pages 205-214

§25 Model Polyhedral Complexes P
Pages 215-223

§26 Singular Complexes S(x). Eilenberg
Pages 224-233

§27 Chain-Homotopies on S(x)
Pages 234-243

§28 Relative Homologies
Pages 244-254

§29 Comparison of the Homology Groups on fa and on fa — pa
Pages 255-266

§30 Type Numbers and Connectivities
Pages 267-277

§31 Normals from a Point to a Manifold
Pages 281-286

§32 Equilibrium Points of an Electrostatic Potential
Pages 287-294

§33 Symmetric Squares of Manifolds and Critical Chords
Pages 295-311

§34 The Symmetric Square of an n-Sphere
Pages 312-317

§35 The Complex Projective n-Space CPn
Pages 318-323

§36 Caps and Saddles
Pages 324-334

§37 The Real Projective n-Space Pn
Pages 335-347

§38 Stein Manifolds. A Theorem of Lefschetz
Pages 348-354

§39 Supplementary Concepts and Theorems
Pages 355-362

Appendix I Preliminary Definitions
Pages 363-365

Appendix II On Elevating Manifold Differentiability
Pages 366-367

Appendix III Singular Homology Theory on Mn Over Z
Pages 368-373

Fundamental Symbols
Pages 374-379

Bibliography Review Article
Pages 380-385

Index of Terms
Pages 387-389