A factorization of the Conway polynomial and covering linkage invariants
| dc.creator | Tsukamoto, Tatsuya | |
| dc.creator | Yasuhara, Akira | |
| dc.date | 2004-05-25 | |
| dc.date.accessioned | 2026-07-07T05:08:34Z | |
| dc.date.available | 2026-07-07T05:08:34Z | |
| dc.description | J.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.description | 9 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0405481 | |
| dc.identifier | http://arxiv.org/abs/math/0405481 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71316 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 | |
| dc.title | A factorization of the Conway polynomial and covering linkage invariants | |
| dc.type | text |