Abstract
This talk is a report on joint work with A. Vaintrob (12, 13). 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 i n 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 (12). We also discuss the approach via finite type invariants, which allowed us in (13) 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. AMS Classification 57M27; 17B10
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