Abstract
We investigate the twisted Alexander polynomial of a 2-bridge knot associated to a Fox coloring. For several families of 2-bridge knots, including but not limited to, torus knots and genus-one knots, we derive formulae for these twisted Alexander polynomials. We use these formulae to confirm a conjecture of Hirasawa and Murasugi for these knots.
| Original language | American English |
|---|---|
| Pages (from-to) | 1-29 |
| Journal | Journal of Knot Theory and its Ramifications |
| Volume | 22 |
| Issue number | 1 |
| State | Published - 2013 |
Keywords
- Geometric topology
- knot theory
- hyperbolic geometry
Disciplines
- Geometry and Topology