Milnor numbers, Spanning Trees, and the Alexander-Conway Polynomial

Details Milnor numbers, Spanning Trees, and the Alexander-Conway Polynomial Milnor numbers, Spanning Trees, and the Alexander-Conway Polynomial

2001-11-08

arxiv.org/abs/math/0111102v1

Mathematics

Geometric Topology

35 pages

Scientific paper

We study relations between the Alexander-Conway polynomial $\nabla_L$ and Milnor higher linking numbers of links from the point of view of finite-type (Vassiliev) invariants. We give a formula for the first non-vanishing coefficient of $\nabla_L$ of an m-component link L all of whose Milnor numbers $\mu_{i_1... i_p}$ vanish for $p\le n$. We express this coefficient as a polynomial in Milnor numbers of L. Depending on whether the parity of n is odd or even, the terms in this polynomial correspond either to spanning trees in certain graphs or to decompositions of certain 3-graphs into pairs of spanning trees. Our results complement determinantal formulas of Traldi and Levine obtained by geometric methods.

Affiliated with

Also associated with

No associations

Rating

Milnor numbers, Spanning Trees, and the Alexander-Conway Polynomial 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 Milnor numbers, Spanning Trees, and the Alexander-Conway Polynomial, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Milnor numbers, Spanning Trees, and the Alexander-Conway Polynomial will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-539584