Quantum topology

by Kauffman, Louis H.

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Title Statements

Full title :Quantum topology / Louis H. Kauffman, Randy A. Baadhio.

Summary

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.

Edition Statements

Publication Date:©1993.

Publication Statements

Publisher(s):World Scientific
Place of Publication:Singapore
Language:eng
Publication Date:©1993.

The Physical Object

Description:1 online resource (xii, 375 pages) : : illustrations

Edition Identifiers

ISBN:9789812796387, 981279638X
oclc:ocn826658007
LC Classification:QA611
Dewey Decimal:514/.224

CONTENTS -- PREFACE -- Introduction to Quantum Topology -- I. Introduction -- II. Quantum Mechanics and Topology -- III. The Temperley Lieb Algebra -- IV. Temperley Lieb Recoupling Theory -- V. The Bracket Polynomial Model for the Jones Polynomial -- VI. Links and Invariants of 3-Manifolds -- VII. The Shadow World -- VIII. On Manifolds With The Same Invariants -- IX. Encirclement and Invariants of 4-Manifolds -- XI. The Turaev-Viro Invariant and Quantum Gravity -- References -- Knot Theory, Exotic Spheres And Global Gravitational Anomalies -- I. Introduction

II. Global Gravitational Anomalies in Topological Field TheoryIII. Knot Theory, Exotic Spheres and Global Anomalies -- IV. Acknowledgments -- V. References -- A DIAGRAMMATIC THEORY OF KNOTTED SURFACES -- Part I. Diagrammatic Approaches to Knotted Surfaces -- 1 Projections -- 1.1 Knotted surface diagrams -- 1.2 Formula for normal Euler number -- 1.3 Seifert algorithms -- 1.4 Diagrammatic algebras -- diamonds -- 2 Movies -- 2.1 Visualizations by movies -- 2.2 Movie moves -- 3 Simplex Equations -- 3.1 Planar tetrahedral equations

3.2 Double point equations Part II. Smoothings of Higher Dimensional Knots -- 4 Smoothings of Quadr…