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 Sr,s 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.