In this second edition, the following recent papers have been
added: "Gauss Codes, Quantum Groups and Ribbon Hopf Algebras",
"Spin Networks, Topology and Discrete Physics", "Link Polynomials
and a Graphical Calculus" and "Knots Tangles and Electrical
Networks". An appendix with a discussion on invariants of embedded
graphs and Vassiliev invariants has also been included.This book is
an introduction to knot and link invariants as generalized
amplitudes (vacuum-vacuum 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 has the advantage of providing very direct access to the
algebra and to the combinatorial topology, as well as the physical
ideas. This book is divided into 2 parts: Part I of the book is a
systematic course in knots and physics starting from the ground up.
Part II is a set of lectures on various topics related to and
sometimes based on Part I. Part II also explores some side-topics
such as frictional properties of knots, relations with
combinatorics and knots in dynamical systems.
General
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