Author | Arnold, V. I. author |
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Title | Singularity Theory I [electronic resource] / by V. I. Arnold, V. V. Goryunov, O. V. Lyashko, V. A. Vasil'ev |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-3-642-58009-3 |
Descript | V, 245 p. 1 illus. online resource |
1. Critical Points of Functions -- 1. Invariants of Critical Points -- 2. The Classification of Critical Points -- 3. Reduction to Normal Forms -- 2. Monodromy Groups of Critical Points -- 1. The Picard-Lefschetz Theory -- 2. Dynkin Diagrams and Monodromy Groups -- 3. Complex Monodromy and Period Maps -- 4. The Mixed Hodge Structure in the Vanishing Cohomology -- 5. Simple Singularities -- 6. Topology of Complements of Discriminants of Singularities -- 3. Basic Properties of Maps -- 1. Stable Maps and Maps of Finite Multiplicity -- 2. Finite Determinacy of Map-Germs, and Their Versal Deformations -- 3. The Topological Equivalence -- 4. The Global Theory of Singularities -- 1. Thom Polynomials for Maps of Smooth Manifolds -- 2. Integer Characteristic Classes and Universal Complexes of Singularities -- 3. Multiple Points and Multisingularities -- 4. Spaces of Functions with Critical Points of Mild Complexity -- 5. Elimination of Singularities and Solution of Differential Conditions -- 6. Tangential Singularities and Vanishing Inflexions -- References -- Author Index