The Mathematics of Knots

by Banagl, Markus; Vogel, Denis

• ISBN13: 9783642156366
• ISBN10: 3642156363
• Format: Hardcover
• Copyright: 2010-12-28
• Publisher: Springer Verlag

Summary

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 physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text.The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.

Table of Contents

Knots, Singular Embeddings, and Monodromy	p. 1
Lower Bounds on Virtual Crossing Number and Minimal Surface Genus	p. 31
A Survey of Twisted Alexander Polynomials	p. 45
On Two Categorifications of the Arrow Polynomial for Virtual Knots	p. 95
An Adelic Extension of the Jones Polynomial	p. 125
Legendrian Grid Number One Knots and Augmentations of their Differential Algebras	p. 143
Embeddings of Four-valent Framed Graphs into 2-surfaces	p. 169
Geometric Topology and Field Theory on 3-Manifolds	p. 199
From Goeritz Matrices to Quasi-alternating Links	p. 257
An Overview of Property 2R	p. 317
DNA, Knots and Tangles	p. 327
Workshop Talks	p. 355
Table of Contents provided by Ingram. All Rights Reserved.