Annals of Mathematics Studies

2 primary works • 4 total works

On Knots. (AM-115)

by Louis H. Kauffman

Published 2 March 2016

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)

by Louis H. Kauffman and Sostenes Lins

Published 2 March 2016

Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134

by Louis H. Kauffman and Sostenes Lins

Published 25 July 1994

This is a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose.

On Knots. (AM-115), Volume 115

by Louis H. Kauffman

Published 21 October 1987

On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial.



Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.