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A Quantum Obstruction to Embedding
by
Joanna Kania-Bartoszynska
Boise State University
Coauthors: Charlie Frohman
The Jones polynomial of a link was introduced in the mid 1980's. It was defined as the normalized trace of an element of a braid group, corresponding to the link, in a certain representation. Shortly after its introduction, the need for a cut and paste theory to explain the Jones polynomial became understood. Witten realized such a theory using ideas from quantum field theory. His construction of topological quantum field theory rested on deep physical intuitions. In addition to explaining the Jones polynomial, Witten's theory produced a whole new realm of three-manifold invariants.
Although the study of 3-manifold invariants is substantial in itself, few applications to classical 3-manifold topology have been found. We use quantum invariants to develop obstructions to embedding one 3-manifold in another. I will describe these obstruction and illustrate their use with examples.
Date received: December 1, 2000
Copyright © 2000 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 # cafy-07.