A factorization of the Conway polynomial and covering linkage invariants

dc.creatorTsukamoto, Tatsuya
dc.creatorYasuhara, Akira
dc.date2004-05-25
dc.date.accessioned2026-07-07T05:08:34Z
dc.date.available2026-07-07T05:08:34Z
dc.descriptionJ.P. Levine showed that the Conway polynomial of a link is a product of two factors: one is the Conway polynomial of a knot which is obtained from the link by banding together the components; and the other is determined by the $\barμ$-invariants of a string link with the link as its closure. We give another description of the latter factor: the determinant of a matrix whose entries are linking pairings in the infinite cyclic covering space of the knot complement, which take values in the quotient field of ${\Bbb Z}[t,t^{-1}]$. In addition, we give a relation between the Taylor expansion of a linking pairing around $t=1$ and derivation on links which is invented by T.D. Cochran. In fact, the coefficients of the powers of $t-1$ will be the linking numbers of certain derived links in $S^3$. Therefore, the first non-vanishing coefficient of the Conway polynomial is determined by the linking numbers in $S^3$. This generalizes a result of J. Hoste.
dc.description9 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0405481
dc.identifierhttp://arxiv.org/abs/math/0405481
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71316
dc.subjectGeometric Topology
dc.subject57M25
dc.titleA factorization of the Conway polynomial and covering linkage invariants
dc.typetext

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