Differential Topology

1 : Manifolds and Maps. - 0. Submanifolds of ?n+k. - 1. Differential Structures. - 2. Differentiable Maps and the Tangent Bundle. - 3. Embeddings and Immersions. - 4. Manifolds with Boundary. - 5. A Convention. - 2 : Function Spaces. - 1. The Weak and Strong Topologies on Cr(M N). - 2. Approximations. - 3. Approximations on ?-Manifolds and Manifold Pairs. - 4. Jets and the Baire Property. - 5. Analytic Approximations. - 3 : Transversality. - 1. The Morse-Sard Theorem. - 2. Transversality. - 4 : Vector Bundles and Tubular Neighborhoods. - 1. Vector Bundles. - 2. Constructions with Vector Bundles. - 3. The Classification of Vector Bundles. - 4. Oriented Vector Bundles. - 5. Tubular Neighborhoods. - 6. Collars and Tubular Neighborhoods of Neat Submanifolds. - 7. Analytic Differential Structures. - 5 : Degrees Intersection Numbers and the Euler Characteristic. - 1. Degrees of Maps. - 2. Intersection Numbers and the Euler Characteristic. - 3. Historical Remarks. - 6 : Morse Theory. - 1. Morse Functions. - 2. Differential Equations and Regular Level Surfaces. - 3. Passing Critical Levels and Attaching Cells. - 4. CW-Complexes. - 7 : Cobordism. - 1. Cobordism and Transversality. - 2. The Thorn Homomorphism. - 8 : Isotopy. - 1. Extending Isotopies. - 2. Gluing Manifolds Together. - 3. Isotopies of Disks. - 9 : Surfaces. - 1. Models of Surfaces. - 2. Characterization of the Disk. - 3. The Classification of Compact Surfaces. Language: English