Series on Knots and Everything - Vol. 3
QUANTUM TOPOLOGY
edited by Louis H Kauffman (University of Illinois at Chicago) & Randy A Baadhio (Lawrence Berkeley Laboratory & University of California at Berkeley)
This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.
This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.
This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.
Contents:
- Introduction to Quantum Topology (L H Kauffman)
- Knot Theory, Exotic
Spheres and Global Gravitational Anomalies (R A Baadhio)
- A Diagrammatic Theory of Knotted Surfaces (J S Carter & M Saito)
- A Categorical Construction of 4D Topological Quantum Field Theories (L Crane & D Yetter)
- Evaluating the Crane-Yetter Invariant (L Crane, L H Kauffman & D Yetter)
- A Method for Computing the Arf Invariants of Links (P Gilmer)
- Triangulations, Categories and Extended Topological Field Theories (R J Lawrence)
- The Casson Invariant for Two-Fold Branched Covers of Links (D Mullins)
- Elementary Conjectures in Classical Knot Theory (J H Przytycki)
- Knot Polynomials as States of Nonperturbative Four Dimensional Quantum Gravity (J Pullin)
- On Invariants of 3-Manifolds Derived from Abelian Groups (J Mattes, M M Polyak & N Reshetikhin)
- and other papers
Readership: Mathematicians and mathematical physicists.
| 392pp |
Pub. date: Sept 1993 |
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