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1 results

  • Vassiliev invariants of quasipositive knots

  • Sebastian Baader
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 5 / September 2006
    Published online by Cambridge University Press:
    25 September 2006, pp. 1343-1350
    Print publication:
    September 2006
    • Article
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  • Quasipositive knots are transverse intersections of complex plane curves with the standard sphere $S^3 \subset {\mathbb C}^2$. It is known that any Alexander polynomial of a knot can be realized by a quasipositive knot. As a consequence, the Alexander polynomial cannot detect quasipositivity. In this paper we prove a similar result about Vassiliev invariants: for any oriented knot $K$ and any natural number $n$ there exists a quasipositive knot $Q$ whose Vassiliev invariants of order less than or equal to $n$ coincide with those of $K$.