Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 (eBook)

David Eisenbud, Walter D. Neumann (Autoren)

eBook Download: PDF

2016 | 1. Auflage
180 Seiten
Princeton University Press (Verlag)
978-1-4008-8192-5 (ISBN)

Infos

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 "e;splicing"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 2.3.2016
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Schlagworte: 3-sphere • Alexander Grothendieck • Alexander polynomial • Algebraic Curve • algebraic equation • Algebraic Geometry • algebraic surface • algorithm • Ambient space • analytic function • Approximation • Big O notation • Call Graph • Cartesian coordinate system • Characteristic Polynomial • Closed-form expression • cohomology • Computation • conjecture • Connected sum • Contradiction • Coprime integers • corollary • Curve • Cyclic group • Determinant • Diagram (category theory) • diffeomorphism • Dimension • Disjoint union • Eigenvalues and Eigenvectors • Equation • equivalence class • Euler number • existential quantification • Exterior (topology) • fiber bundle • fibration • foliation • fundamental group • Geometry • Graph (discrete mathematics) • Ground field • Homeomorphism • homology sphere • Identity matrix • Integer matrix • Intersection form (4-manifold) • Isolated point • Isolated singularity • Jordan normal form • knot theory • Mathematical Induction • Monodromy • monodromy matrix • Natural transformation • Newton Polygon • Newton's method • Normal (geometry) • Notation • N-sphere • pairwise • parametrization • Plane curve • polynomial • power series • projective plane • Puiseux series • Quantity • rational function • Resolution of Singularities • Riemann sphere • Riemann surface • Root of unity • scientific notation • Seifert Surface • Set (mathematics) • Sign (mathematics) • Solid torus • Special case • stereographic projection • submanifold • Summation • Theorem • Three-dimensional space (mathematics) • Topology • torus • Torus knot • Tubular neighborhood • Unit circle • Unit vector • unknot • Variable (mathematics)
• ISBN-10: 1-4008-8192-7 / 1400881927
• ISBN-13: 978-1-4008-8192-5 / 9781400881925