The Alexander polynomial of (1,1)-knots
| dc.creator | Cattabriga, Alessia | |
| dc.date | 2005-01-23 | |
| dc.date | 2005-10-21 | |
| dc.date.accessioned | 2026-07-07T06:39:20Z | |
| dc.date.available | 2026-07-07T06:39:20Z | |
| dc.description | In this paper we investigate the Alexander polynomial of (1,1)-knots, which are knots lying in a 3-manifold with genus one at most, admitting a particular decomposition. More precisely, we study the connections between the Alexander polynomial and a polynomial associated to a cyclic presentation of the fundamental group of an n-fold strongly-cyclic covering branched over the knot, which we call the n-cyclic polynomial. In this way, we generalize to all (1,1)-knots, with the only exception of those lying in S^2\times S^1, a result obtained by J. Minkus for 2-bridge knots and extended by the author and M. Mulazzani to the case of (1,1)-knots in the 3-sphere. As corollaries some properties of the Alexander polynomial of knots in the 3-sphere are extended to the case of (1,1)-knots in lens spaces. | |
| dc.description | 11 pages, 1 figure. A corollary has been extended, and a new example added. Accepted for publication on J. Knot Theory Ramifications | |
| dc.identifier | https://arxiv.org/abs/math/0501394 | |
| dc.identifier | http://arxiv.org/abs/math/0501394 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101037 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M12, 57M27 | |
| dc.title | The Alexander polynomial of (1,1)-knots | |
| dc.type | text |