arXiv:math/0412453 Abstract

arXiv:math/0412453 [math.GT]Abstract References Reviews Resources

A note on Vassiliev invariants of quasipositive knots

Published 2004-12-22, updated 2005-04-13Version 2

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.

Comments: 7 pages, 7 figures, one erroneous statement removed, more details in proof

Categories: math.GT

Subjects: 57M25

Keywords: vassiliev invariants, quasipositive knot, alexander polynomial, detect quasipositivity, natural number

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