Matrix-tree theorems and the Alexander-Conway polynomial

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dc.creatorMasbaum, Gregor
dc.date2002-11-04
dc.date.accessioned2026-07-07T04:52:38Z
dc.date.available2026-07-07T04:52:38Z
dc.descriptionThis 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.
dc.descriptionPublished by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper13.abs.html
dc.identifierhttps://arxiv.org/abs/math/0211063
dc.identifierhttp://arxiv.org/abs/math/0211063
dc.identifierGeom. Topol. Monogr. 4 (2002) 201-214
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65540
dc.subjectCombinatorics
dc.subjectGeometric Topology
dc.subject57M27, 17B10
dc.titleMatrix-tree theorems and the Alexander-Conway polynomial
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