Regular Seifert surfaces and Vassiliev knot invariants

Details Regular Seifert surfaces and Vassiliev knot invariants Regular Seifert surfaces and Vassiliev knot invariants

1998-04-06

arxiv.org/abs/math/9804032v2

Mathematics

Geometric Topology

54 pages. Exposition extensively revised

Scientific paper

We show that the Vassiliev invariants of orders $\leq n$ 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. As a consequence of this, we obtain that the Vassiliev invariants of the knot $K=\partial S$ are null-concordance obstructions of certain links that can be obtained from regular spines of S. We also discuss various generalizations of these results, and we conjecture a geometric characterization of knots whose invariants of all orders vanish.

Affiliated with

Also associated with

No associations

Rating

Regular Seifert surfaces and Vassiliev knot invariants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Regular Seifert surfaces and Vassiliev knot invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regular Seifert surfaces and Vassiliev knot invariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-434151