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.
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.
Über den Autor
Alexandru Dimca is a world-leading authority in Singularity Theory and Hyperplane Arrangements, with a strong track record of ground-breaking research. He is the author of four books and over 120 research papers, many of them devoted to the topics discussed in this book. He has an established reputation for his clear writing style, and his vast teaching experience helps him to convey the main ideas in an accessible and efficient way.
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.
