# Books written by Vaughan F. R. Jones.

Sir Vaughan Frederick Randal Jones is a New Zealand mathematician, known for his work on von Neumann algebras and knot polynomials. He was awarded a Fields Medal in 1990 "For his discovery of an unexpected link between the mathematical study of knots – a field that dates back to the 19th century – and statistical mechanics, a form of mathematics used to study complex systems with large numbers of components."

## Knots, Low-Dimensional Topology and Applications

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function.

## Coxeter Graphs and Towers of Algebras

Our subject is certain algebraic and von Neumann algebraic topics closely related to the original paper. However, in order to promote, in a modest way, the contact between diverse fields of mathematics, we have tried to make this work accessible to the broadest audience. Consequently, this book contains much elementary expository material.

## Subfactors and Knots

Provides an extensive introduction to the theory of von Neumann algebras and to knot theory and braid groups. The presentation follows the historical development of the theory of subfactors and the ensuing applications to knot theory, including full proofs of some of the major results.

## Knots at Hellas 98

Proceedings of the International Conference on Knot Theory and Its Ramifications

## Introduction to Subfactors

These notes give an introduction to the subject suitable for a student who has only a little familiarity with the theory of Hilbert space. Subfactors have been a subject of considerable research activity for about fifteen years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory.