This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.
The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.
In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.
Readership: Physicists and mathematicians.
Author(s): Louis H Kauffman
Series: Series on Knots and Everything Vol. 53
Edition: 4
Publisher: World Scientific
Year: 2013
Language: English
Pages: C, XVIII, 846
Tags: Mathematics/Geometry & Topology;Mathematical Physics /Graph Theory
Physical Knots
States and the Bracket Polynomial
The Jones Polynomial and Its Generalizations
Braids and the Jones Polynomial
Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q
Yang-Baxter Models for Specializations of the Homfly Polynomial
Knot-Crystals — Classical Knot Theory in a Modern Guise
The Kauffman Polynomial
Three Manifold Invariants from the Jones Polynomial
Integral Heuristics and Witten's Invariants
The Chromatic Polynomial
The Potts Model and the Dichromatic Polynomial
The Penrose Theory of Spin Networks
Knots and Strings — Knotted Strings
DNA and Quantum Field Theory
Knots in Dynamical Systems — The Lorenz Attractor
and selected papers
