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.

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