This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical framework, create a context that naturally includes a wide range of interrelated topics in topology and mathematical physics. The author takes ...
This book offers 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 ...
This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in combinatorics. 1983 edition. Includes 51 ...
This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th-century theory of vortex atoms, reprints of modern papers on knotted flux in ...
This volume provides 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 includes a range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial ...
Hopf algebras have proved to be very interesting structures with deep connections to various areas of mathematics, particularly through quantum groups. Indeed, the study of Hopf algebras, their representations, their generalizations, and the categories related to all these objects has an interdisciplinary nature. It finds methods, relationships, ...
This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical framework, create a context that naturally includes a wide range of interrelated topics in topology and mathematical physics. The author takes ...
There were many developments in the area of knot theory in the 1990s. They include Thurston's work on geometric structures on 3-manifolds (such as knot complements), Gordon-Luecke's work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type ...
This work is based on the authors' research on rendering images of higher dimensional fractals by a distance estimation technique. It is self-contained, giving a careful treatment of both the known techniques and the authors' new methods. The distance estimation technique was originally applied to Julia sets and the Mandelbrot set in the complex ...
Discusses topics in the field of quantum topology, including: knot theory, exotic spheres and global gravitational anomolies; construction of 4D topological quantum field theories; computing the arf invariants of links; and the Casson invariants for two-fold branched covers of links.
This volume gathers the contributions from the international conference "Intelligence of Low Dimensional Topology 2006," which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.
Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics. After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and ...
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