Knots, Vassiliev Invariants and Functional Integration without Integration
Louis H. Kauffman
University of Illinois at Chicago
There is a deep inteconnection between invariants of knots and links and the use of functional integrals as a heuristic (they do not exist). We replace the non-existent functional integral by a class of functions of gauge fields: defining F equivalent to G if F-G = DH where F,G,H are functions of a gauge field A that are "rapidly vanishing at infinity" in the sense that they go zero rapidly when an appropriate norm of A goes to infinity. DH denotes a functional derivative of F with respect to one of the gauge coordinates.We then define INT(F) to be the equivalence class of F. The talk will discuss how link invariants and Vassiliev invariants are intertwined with these INTegrals.
Date received: December 12, 2001
Copyright © 2001 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # caip-08.