Singularities and Topology of Hypersurfaces

Singularities and Topology of Hypersurfaces by Alexandru Dimca.

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Bibliographic Details
Main Author:	Dimca, Alexandru (Author)
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	New York, NY : Springer New York : Imprint: Springer, 1992.
Edition:	1st ed. 1992.
Series:	Universitext, Springer eBook Collection.
Subjects:	Algebraic geometry. Algebraic topology. Electronic resources (E-books)
Online Access:	Click to view e-book
Holy Cross Note:	Loaded electronically. Electronic access restricted to members of the Holy Cross Community.

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.