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

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dc.creatorMasbaum, Gregor
dc.creatorVaintrob, Arkady
dc.date2001-11-08
dc.date.accessioned2026-07-07T04:44:28Z
dc.date.available2026-07-07T04:44:28Z
dc.descriptionWe 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 $μ_{i_1... i_p}$ 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.
dc.description35 pages
dc.identifierhttps://arxiv.org/abs/math/0111102
dc.identifierhttp://arxiv.org/abs/math/0111102
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62602
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.subject57M27
dc.titleMilnor numbers, Spanning Trees, and the Alexander-Conway Polynomial
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