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Three-dimensional link theory and invariants of plane curve singularities. (am-110).

Author: David Eisenbud.
Publisher: Princeton : Princeton Univ Press, 2016.
Series: Annals of Mathematics Studies, 110
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David Eisenbud.
ISBN: 1400881927 9781400881925
OCLC Number: 1083156630
Language Note: In English.
Description: 1 online resource
Contents: Frontmatter --
Contents --
Abstract --
Three-Dimensional Link Theory and Invariants of Plane Curve Singularities --
Introduction --
Review --
Preview --
Chapter I: Foundations --
Appendix to Chapter I: Algebraic Links --
Chapter II: Classification --
Chapter III: Invariants --
Chapter IV: Examples --
Chapter V: Relation to Plumbing --
References --
Backmatter.
Series Title: Annals of Mathematics Studies, 110

Abstract:

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.

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