Knot polynomials and Vassiliev's invariants

Summary A fundamental relationship is established between Jones' knot invariants and Vassiliev's knot invariants. Since Vassiliev's knot invariants have a firm grounding in classical topology, one obtains as a result a first step in understanding the Jones polynomial by topological methods.Oblatum 20-V-1991 & 10-VI-1992Research supported in part by NSF Grant DMS-88-055627.Research supported in part by NSF Grant DMS-90-04017.