Mapping Degree Theory

Contents
Preface
I. History
1. Prehistory
2. Inception and formation
3. Accomplishment
4. Renaissance and reformation
5. Axiomatization
6. Further developments
II. Manifolds
1. Differentiable mappings
2. Differentiable manifolds
3. Regular values
4. Tubular neighborhoods
5. Approximation and homotopy
6. Diffeotopies
7. Orientation
III. The Brouwer-Kronecker degree
1. The degree of a smooth mapping
2. The de Rham definition
3. The degree of a continuous mapping
4. The degree of a differentiable mapping
5. The Hopf invariant
6. The Jordan Separation Theorem
7. The Brouwer Theorems
IV. Degree theory in Euclidean spaces
1. The degree of a smooth mapping
2. The degree of a continuous mapping
3. The degree of a differentiable mapping
4. Winding number
5. The Borsuk-Ulam Theorem
6. The Multiplication Formula
7. The Jordan Separation Theorem
V. The Hopf Theorems
1. Mappings into spheres
2. The Hopf Theorem: Brouwer-Kronecker degree
3. The Hopf Theorem: Euclidean degree
4. The Hopf fibration
5. Singularities of tangent vector fields
6. Gradient vector fields
7. The Poincaré-Hopf Index Theorem
Names of mathematicians cited
Historical references
Bibliography
Symbols
Index