Singularities and Topology of Hypersurfaces: Universitext

1 Whitney Stratifications.- 1. Some Motivations and Basic Definitions.- 2. Topological Triviality and ?*-Constant Deformations.- 3. The First Thom Isotopy Lemma.- 4. On the Topology of Affine Hypersurfaces.- 5. Links and Conic Structures.- 6. On Zariski Theorems of Lefschetz Type.- 2 Links of Curve and Surface Singularities.- 1. A Quick Trip into Classical Knot Theory.- 2. Links of Plane Curve Singularities.- 3. Links of Surface Singularities.- 4. Special Classes of Surface Singularities.- 3 The Milnor Fibration and the Milnor Lattice.- 1. The Milnor Fibration.- 2. The Connectivity of the Link, of the Milnor Fiber, and of Its Boundary.- 3. Vanishing Cycles and the Intersection Form.- 4. Homology Spheres, Exotic Spheres, and the Casson Invariant.- 4 Fundamental Groups of Hypersurface Complements.- 1. Some General Results.- 2. Presentations of Groups and Monodromy Relations.- 3. The van Kampen-Zariski Theorem.- 4. Two Classical Examples.- 5 Projective Complete Intersections.- 1. Topology of the Projective Space Pn.- 2. Topology of Complete Intersections.- 3. Smooth Complete Intersections.- 4. Complete Intersections with Isolated Singularities.- 6 de Rham Cohomology of Hypersurface Complements.- 1. Differential Forms on Hypersurface Complements.- 2. Spectral Sequences and Koszul Complexes.- 3. Singularities with a One-Dimensional Critical Locus.- 4. Alexander Polynomials and Defects of Linear Systems.- Appendix A Integral Bilinear Forms and Dynkin Diagrams.- Appendix B Weighted Projective Varieties.- Appendix C Mixed Hodge Structures.- References.