Three-Dimensional Link Theory and Invariants of Plane Curve Singularities

by David Eisenbud, Walter D. Neumann

Overview

This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing.


Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.

Product Details

ISBN-13:	9780691083810
Publisher:	Princeton University Press
Publication date:	01/21/1986
Series:	Annals of Mathematics Studies , #110
Pages:	180
Product dimensions:	6.00(w) x 9.00(h) x (d)

Table of Contents

• Frontmatter, pg. i
• Contents, pg. v
• Abstract, pg. vii
• Three-Dimensional Link Theory and Invariants of Plane Curve Singularities, pg. 1
• Introduction, pg. 3
• Review, pg. 3
• Preview, pg. 14
• Chapter I: Foundations, pg. 20
• Appendix to Chapter I: Algebraic Links, pg. 48
• Chapter II: Classification, pg. 59
• Chapter III: Invariants, pg. 83
• Chapter IV: Examples, pg. 123
• Chapter V: Relation to Plumbing, pg. 134
• References, pg. 169
• Backmatter, pg. 173