Seifert surfaces, Commutators and Vassiliev invariants

Abstract

We show that the Vassiliev invariants of a knot K, are obstructions to finding a regular Seifert surface, S, whose complement looks "simple" (e.g. like the complement of a disc) to the lower central series of its fundamental group.

arXiv comment35 pages, 13 Figures. To appear in the J. of Knot Theory and its Ramifications (special volume in honor of L. Kauffman)