Singularities and Topology of Hypersurfaces

Main Author: Dimca, Alexandru
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 1992, 1992
Edition:1st ed. 1992
Series:Universitext
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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