The Fundamental Theorem of Vassiliev Invariants

Details The Fundamental Theorem of Vassiliev Invariants The Fundamental Theorem of Vassiliev Invariants

1997-02-06

arxiv.org/abs/q-alg/9702009v1

Mathematics

Quantum Algebra

LaTeX2e directory tree, 30 pp

Scientific paper

The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a topological/combinatorial approach following M. Hutchings, a geometrical approach following Kontsevich, an algebraic approach following Drinfel'd's theory of associators, and a physical approach coming from the Chern-Simons quantum field theory. Each of these approaches is unsatisfactory in one way or another, and hence we argue that we still don't really understand the fundamental theorem of Vassiliev invariants.

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