The Mathematics of Knots Theory and Application /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Banagl, Markus (Editor), Vogel, Denis (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Contributions in Mathematical and Computational Sciences ; 1
• Subjects: Mathematics.; Differential geometry.; Topology.; Manifolds (Mathematics).; Complex manifolds.; Biomathematics.; Physics.; Manifolds and Cell Complexes (incl. Diff.Topology).; Differential Geometry.; Physiological, Cellular and Medical Topics.; Numerical and Computational Physics.

The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical ph...

Table of Contents:

• Preface
• 1 Knots, Singular Embeddings, and Monodromy
• 2 Lower Bounds on Virtual Crossing Number and Minimal Surface Genus
• 3 A Survey of Twisted Alexander Polynomials
• 4 On Two Categorifications of the Arrow Polynomial for Virtual Knots
• 5 An Adelic Extension of the Jones Polynomial
• 6 Legendrian Grid Number One Knots and Augmentations of their Differential Algebras
• 7 Embeddings of Four-Valent Framed Graphs into 2-Surfaces
• 8 Geometric Topology and Field Theory on 3-Manifolds
• 9 From Goeritz Matrices to Quasi-Alternating Links
• 10 An Overview of Property 2R
• 11 DNA, Knots and Tangles.