Stable mappings and their singularities

M. Golubitsky, V. Guillemin

[目次]

  • I: Preliminaries on Manifolds.- x1. Manifolds.- x2. Differentiable Mappings and Submanifolds.- x3. Tangent Spaces.- x4. Partitions of Unity.- x5. Vector Bundles.- x6. Integration of Vector Fields.- II: Transversality.- x1. Sard's Theorem.- x2. Jet Bundles.- x3. The Whitney C? Topology.- x4. Transversality.- x5. The Whitney Embedding Theorem.- x6. Morse Theory.- x7. The Tubular Neighborhood Theorem.- III: Stable Mappings.- x1. Stable and Infinitesimally Stable Mappings.- x2. Examples.- x3. Immersions with Normal Crossings.- x4. Submersions with Folds.- IV: The Malgrange Preparation Theorem.- x1. The Weierstrass Preparation Theorem.- x2. The Malgrange Preparation Theorem.- x3. The Generalized Malgrange Preparation Theorem.- V: Various Equivalent Notions of Stability.- x1. Another Formulation of Infinitesimal Stability.- x2. Stability Under Deformations.- x3. A Characterization of Trivial Deformations.- x4. Infinitesimal Stability => Stability.- x5. Local Transverse Stability.- x6. Transverse Stability.- x7. Summary.- VI: Classification of Singularities, Part I: The Thom-Boardman Invariants.- x1. The Sr Classification.- x2. The Whitney Theory for Generic Mappings between 2-Manifolds.- x3. The Intrinsic Derivative.- x4. The Sr,s Singularities.- x5. The Thom-Boardman Stratification.- x6. Stable Maps Are Not Dense.- VII: Classification of Singularities, Part II: The Local Ring of a Singularity.- x1. Introduction.- x2. Finite Mappings.- x3. Contact Classes and Morin Singularities.- x4. Canonical Forms for Morin Singularities.- x5. Umbilics.- x6. Stable Mappings in Low Dimensions.- xA. Lie Groups.- Symbol Index.

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この本の情報

書名 Stable mappings and their singularities
著作者等 Golubitsky, Martin
Guillemin, Victor
Golubitsky M.
シリーズ名 Graduate texts in mathematics
出版元 Springer-Verlag
刊行年月 c1973
版表示 Softcover reprint of the original 1st ed. 1973
ページ数 x, 209 p.
大きさ 25 cm
ISBN 038790073X
3540900721
354090073X
0387900721
NCID BA03400133
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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