Singularity Theory I

• 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.

From the reviews: " My general impression is of a particularly nice book, with a well-balanced bibliography. Recommended!" Mededelingen van Het Wiskundig Genootschap, 1995 "The authors offer here an up- to- date guide to the topic and its main applications, including a number of new results. It is very convenient for the reader... a carefully prepared and extensive bibliography makes it easy to find the necessary details when needed. The books (EMS 6 and EMS 39) describe a lot of interesting topics. Both volumes are a very valuable addition to the library of any mathematician or physicist interested in modern mathematical analysis." European Mathematical Society Newsletter, 1994