Parameterizations of 1-bridge torus knots
| dc.creator | Choi, Doo Ho | |
| dc.creator | Ko, Ki Hyoung | |
| dc.date | 2001-12-11 | |
| dc.date | 2002-01-03 | |
| dc.date.accessioned | 2026-07-07T04:45:10Z | |
| dc.date.available | 2026-07-07T04:45:10Z | |
| dc.description | A 1-bridge torus knot in a 3-manifold of genus $\le 1$ is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert's normal form and the Conway's normal form for 2-bridge knots. For a given Schubert's normal form we give algorithms to determine the number of components and to compute the fundamental group of the complement when the normal form determines a knot. We also give a description of the double branched cover of an ambient 3-manifold branched along a 1-bridge torus knot by using its Conway's normal form and obtain an explicit formula for the first homology of the double cover. | |
| dc.description | 26 pages, 28 figures, a minor revision | |
| dc.identifier | https://arxiv.org/abs/math/0112102 | |
| dc.identifier | http://arxiv.org/abs/math/0112102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62863 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25; 57M12 | |
| dc.title | Parameterizations of 1-bridge torus knots | |
| dc.type | text |