A note on Vassiliev invariants of quasipositive knots

Details A note on Vassiliev invariants of quasipositive knots A note on Vassiliev invariants of quasipositive knots

2004-12-22

arxiv.org/abs/math/0412453v2

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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