Singularities and Topology of Hypersurfaces

Inhaltsverzeichnis

• 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.