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Knot polynomials and Vassiliev's invariants

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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.

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Authors and Affiliations

  1. Department of Mathematics, Columbia University, 10027, New York, NY, USA

    Joan S. Birman & Xiao-Song Lin

Authors
  1. Joan S. Birman
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  2. Xiao-Song Lin
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Additional information

Oblatum 20-V-1991 & 10-VI-1992

Research supported in part by NSF Grant DMS-88-055627.

Research supported in part by NSF Grant DMS-90-04017.

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Birman, J.S., Lin, XS. Knot polynomials and Vassiliev's invariants. Invent Math 111, 225–270 (1993). https://doi.org/10.1007/BF01231287

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