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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.
Contents:- 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
Readership: Physicists and mathematicians.
- Sales Rank: #2501902 in eBooks
- Published on: 2012-11-09
- Released on: 2012-11-09
- Format: Kindle eBook
Review
"This book is an essential volume for the student of low-dimensional topology from which a serious student can learn most aspects of modern knot theory. Its informal tone encourages investigation on the part of the reader. The author leaves the reader items to puzzle out. " -- Mathematical Reviews
Reviews of the Third Edition:
"It is an attractive book for physicists with profuse and often entertaining illustrations ... proofs ... seldom heavy and nearly always well explained with pictures ... succeeds in infusing his own excitement and enthusiasm for these discoveries and their potential implications." -- Physics Today
"The exposition is clear and well illustrated with many examples. The book can be recommended to everyone interested in the connections between physics and topology of knots." -- Mathematics Abstracts
"... here is a gold mine where, with care and patience, one should get acquainted with a beautiful subject under the guidance of a most original and imaginative mind." -- Mathematical Reviews
"The exposition is clear and well illustrated with many examples. The book can be recommended to everyone interested in the connections between physics and topology of knots." --Mathematics Abstracts
"… here is a gold mine where, with care and patience, one should get acquainted with a beautiful subject under the guidance of a most original and imaginative mind." --Mathematical Reviews
From the Inside Flap
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, articles on other topics, including Khovanov Homology, have been included.
About the Author
Louis Kauffman was born in 1945. He graduated as valedictorian of his class at Norwood Norfolk Central High School in 1962. He received his BS at MIT in 1966 and his PhD in mathematics from Princeton University in 1972. Kauffman has been a prominent leader in Knot Theory, one of the most active research areas in mathematics today. His discoveries include a state sum model for the Alexander-Conway Polynomial, the bracket state sum model for the Jones polynomial, the Kauffman polynomial and Virtual Knot Theory. He is the Editor-in-Chief of JKTR, Editor of the Series on Knots and Everything, full professor at UIC and author of numerous books related to the theory of knots — including Knots and Physics", "Knots and Applications", "On Knots", and "Formal Knot Theory".
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