Oh, what a tangled web . . . Everything should have been quiet and pleasant for Ben Holiday, the former Chicago lawyer who became sovereign of the Magic Kingdom of Landover. But it wasn’t. Horris Kew, conjurer, confidence-man, and trickster, had returned to Landover from Ben’s own world. Alas, Horris had not returned of his own volition—he had been sent by the Gorse, a sorcerer of great evil, whom Horris had unwittingly freed from the magic Tangle Box, where it had long ago been imprisoned by the fairy folk. Now it had returned to enslave those who had once dared condemn it. But first, it would rid Landover of all who could stand in its way. . . . Soon Ben found himself imprisoned within the gloom of the Tangle Box, lost in its mists and its labyrinthine ways. The only one who could free Ben from the Tangle Box was the lady Willow. But she had disappeared, was gone from Landover on a mysterious mission of her own. . . .

OH, WHAT A TANGLED WEB... Everything should have been quiet and pleasant for Ben Holiday, the former Chicago lawyer who became sovereign of the Magic Kingdom of Landover. But it wasn't. Horris Kew, conjurer, confidence-man, and trickster, had returned to Landover from Ben's own world. Alas, Horris had not returned of his own volition--he had been sent by the Gorse, a sorcerer of great evil, whom Horris had unwittingly freed from the magic Tangle Box, where it had long ago been imprisoned by the fairy folk. Now it had returned to enslave those who had once dared condemn it. But first, it would rid Landover of all who could stand in its way... Soon Ben found himself imprisoned within the gloom of the Tangle Box, lost in its mists and its labyrinthine ways. The only one who could free Ben from the Tangle Box was the lady Willow. But she had disappeared, was gone from Landover on a mysterious mission of her own....

This invaluable book is an introduction to knot and link invariants as generalised 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 a 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 third edition, a paper by the author entitled "Functional Integration and Vassiliev invariants" has been added. This paper shows how the Kontsevich integral approach to the Vassiliev invariants is directly related to the perturbative expansion of Witten's functional integral. While the book supplies the background, this paper can be read independently as an introduction to quantum field theory and knot invariants and their relation to quantum gravity. As in the second edition, there is a selection of papers by the author at the end of the book. Numerous clarifying remarks have been added to the text.

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.

In this thesis, the author develops numerical techniques for tracking and characterising the convoluted nodal lines in three-dimensional space, analysing their geometry on the small scale, as well as their global fractality and topological complexity---including knotting---on the large scale. The work is highly visual, and illustrated with many beautiful diagrams revealing this unanticipated aspect of the physics of waves. Linear superpositions of waves create interference patterns, which means in some places they strengthen one another, while in others they completely cancel each other out. This latter phenomenon occurs on 'vortex lines' in three dimensions. In general wave superpositions modelling e.g. chaotic cavity modes, these vortex lines form dense tangles that have never been visualised on the large scale before, and cannot be analysed mathematically by any known techniques.

Relates a tale about the magical kingdom of Landover, where mirth and mayhem, wizardry and wit rule.

The motivations, goals and general culture of theoretical physics and mathematics are different. Most practitioners of either discipline have no necessity for most of the time to keep abreast of the latest developments in the other. However on occasion newly developed mathematical concepts become relevant in theoretical physics and the less rigorous theoretical physics framework may prove valuable in understanding and suggesting new theorems and approaches in pure mathematics. Such interdis ciplinary successes invariably cause much rejoicing, as over a prodigal son returned. In recent years the framework provided by quantum field theory and functional in tegrals, developed over half a century in theoretical physics, have proved a fertile soil for developments in low dimensional topology and especially knot theory. Given this background it was particularly pleasing that NATO was able to generously sup port an Advanced Research Workshop to be held in Cambridge, England from 6th to 12th September 1992 with the title Low Dimensional Topology and Quantum Field Theory. Although independently organised this overlapped as far as some speak ers were concerned with a longer term programme with the same title organised by Professor M Green, Professor E Corrigan and Dr R Lickorish. The contents of this proceedings of the workshop demonstrate the breadth of topics now of interest on the interface between theoretical physics and mathematics as well as the sophistication of the mathematical tools required in current theoretical physics.

This volume includes both rigorous asymptotic results on the inevitability of random knotting and linking, and Monte Carlo simulations of knot probability at small lengths. The statistical mechanics and topology of surfaces on the d-dimensional simple cubic lattice are investigated. The energy of knots is studied both analytically and numerically. Vassiliev invariants are investigated and used in random knot simulations. A mutation scheme which leaves the Jones polynomial unaltered is described. Applications include the investigation of RNA secondary structure using Vassiliev invariants, and the direct experimental measurement of DNA knot probability as a function of salt concentration in random cyclization experiments on linear DNA molecules. The papers in this volume reflect the diversity of interest across science and mathematics in this subject, from topology to statistical mechanics to theoretical chemistry to wet-lab molecular biology.