2002/11/04 by Gregor Masbaum
Mathematics · #math.CO #math.GT #msc:57M27 #msc:17B10
published as Geom. Topol. Monogr. 4 (2002) 201-214 · Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper13.abs.html
arxiv created 2002/11/04 · arxiv updated 2009/11/30
This talk is a report on joint work with A. Vaintrob [arXiv:math.CO/0109104 and math.GT/0111102]. It is organised as follows. We begin by recalling how the classical Matrix-Tree Theorem relates two different expressions for the lowest degree coefficient of the Alexander-Conway polynomial of a link. We then state our formula for the lowest degree coefficient of an algebraically split link in terms of Milnor's triple linking numbers. We explain how this formula can be deduced from a determinantal expression due to Traldi and Levine by means of our Pfaffian Matrix-Tree Theorem [arXiv:math.CO/0109104]. We also discuss the approach via finite type invariants, which allowed us in [arXiv:math.GT/0111102] to obtain the same result directly from some properties of the Alexander-Conway weight system. This approach also gives similar results if all Milnor numbers up to a given order vanish.