Author | Golubitsky, Martin. author |
---|---|
Title | Stable Mappings and Their Singularities [electronic resource] / by Martin Golubitsky, Victor Guillemin |
Imprint | New York, NY : Springer US, 1973 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-7904-5 |
Descript | 209 p. online resource |
I: Preliminaries on Manifolds -- ยง1. Manifolds -- ยง2. Differentiable Mappings and Submanifolds -- ยง3. Tangent Spaces -- ยง4. Partitions of Unity -- ยง5. Vector Bundles -- ยง6. Integration of Vector Fields -- II: Transversality -- ยง1. Sardโs Theorem -- ยง2. Jet Bundles -- ยง3. The Whitney C? Topology -- ยง4. Transversality -- ยง5. The Whitney Embedding Theorem -- ยง6. Morse Theory -- ยง7. The Tubular Neighborhood Theorem -- III: Stable Mappings -- ยง1. Stable and Infinitesimally Stable Mappings -- ยง2. Examples -- ยง3. Immersions with Normal Crossings -- ยง4. Submersions with Folds -- IV: The Malgrange Preparation Theorem -- ยง1. The Weierstrass Preparation Theorem -- ยง2. The Malgrange Preparation Theorem -- ยง3. The Generalized Malgrange Preparation Theorem -- V: Various Equivalent Notions of Stability -- ยง1. Another Formulation of Infinitesimal Stability -- ยง2. Stability Under Deformations -- ยง3. A Characterization of Trivial Deformations -- ยง4. Infinitesimal Stability => Stability -- ยง5. Local Transverse Stability -- ยง6. Transverse Stability -- ยง7. Summary -- VI: Classification of Singularities, Part I: The Thom-Boardman Invariants -- ยง1. The Sr Classification -- ยง2. The Whitney Theory for Generic Mappings between 2-Manifolds -- ยง3. The Intrinsic Derivative -- ยง4. The Sr,s Singularities -- ยง5. The Thom-Boardman Stratification -- ยง6. Stable Maps Are Not Dense -- VII: Classification of Singularities, Part II: The Local Ring of a Singularity -- ยง1. Introduction -- ยง2. Finite Mappings -- ยง3. Contact Classes and Morin Singularities -- ยง4. Canonical Forms for Morin Singularities -- ยง5. Umbilics -- ยง6. Stable Mappings in Low Dimensions -- ยงA. Lie Groups -- Symbol Index