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.
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