Eisenbud / Neumann Three-Dimensional Link Theory and Invariants of Plane Curve Singularities

1. Auflage 2016
ISBN: 978-1-4008-8192-5
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 110, 180 Seiten

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

Eisenbud, David

Neumann, Walter D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

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