Mathematics – Geometric Topology
Scientific paper
2004-12-22
Mathematics
Geometric Topology
7 pages, 7 figures, one erroneous statement removed, more details in proof
Scientific paper
It has been 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.
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