Author | Hirsch, Morris W. author |
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Title | Differential Topology [electronic resource] / by Morris W. Hirsch |
Imprint | New York, NY : Springer New York, 1976 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9449-5 |
Descript | X, 222 p. online resource |
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