Stable Mappings and Their Singularities

I: Preliminaries on Manifolds. - 1. Manifolds. - 2. Differentiable Mappings and Submanifolds. - 3. Tangent Spaces. - 4. Partitions of Unity. - 5. Vector Bundles. - 6. Integration of Vector Fields. - II: Transversality. - 1. Sard's Theorem. - 2. Jet Bundles. - 3. The Whitney C? Topology. - 4. Transversality. - 5. The Whitney Embedding Theorem. - 6. Morse Theory. - 7. The Tubular Neighborhood Theorem. - III: Stable Mappings. - 1. Stable and Infinitesimally Stable Mappings. - 2. Examples. - 3. Immersions with Normal Crossings. - 4. Submersions with Folds. - IV: The Malgrange Preparation Theorem. - 1. The Weierstrass Preparation Theorem. - 2. The Malgrange Preparation Theorem. - 3. The Generalized Malgrange Preparation Theorem. - V: Various Equivalent Notions of Stability. - 1. Another Formulation of Infinitesimal Stability. - 2. Stability Under Deformations. - 3. A Characterization of Trivial Deformations. - 4. Infinitesimal Stability => Stability. - 5. Local Transverse Stability. - 6. Transverse Stability. - 7. Summary. - VI: Classification of Singularities Part I: The Thom-Boardman Invariants. - 1. The Sr Classification. - 2. The Whitney Theory for Generic Mappings between 2-Manifolds. - 3. The Intrinsic Derivative. - 4. The Srs Singularities. - 5. The Thom-Boardman Stratification. - 6. Stable Maps Are Not Dense. - VII: Classification of Singularities Part II: The Local Ring of a Singularity. - 1. Introduction. - 2. Finite Mappings. - 3. Contact Classes and Morin Singularities. - 4. Canonical Forms for Morin Singularities. - 5. Umbilics. - 6. Stable Mappings in Low Dimensions. - A. Lie Groups. - Symbol Index. Language: English