Milnor numbers, spanning trees, and the Alexander–Conway polynomial |
| |
Authors: | Gregor Masbaum Arkady Vaintrob |
| |
Affiliation: | a Institut de Mathématiques de Jussieu, Equipe ‘Topologie et géométrie algébriques’, Case 7012, Université Paris VII, 75251, Paris Cedex 05, France;b Department of Mathematics, University of Oregon, Eugene, OR 97405, USA |
| |
Abstract: | We study relations between the Alexander–Conway polynomial 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 L of an m-component link L all of whose Milnor numbers μi1…ip vanish for pn. 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. |
| |
Keywords: | Alexander– Conway polynomial Milnor numbers Vassiliev invariants Spanning trees |
本文献已被 ScienceDirect 等数据库收录! |
|