The Alexander polynomial of twisted torus knots
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918137774997504 |
|---|---|
| author | Adnan Park, Kyungbae |
| author_facet | Adnan Park, Kyungbae |
| contents | Twisted torus knots are a generalization of torus knots, obtained by introducing additional full twists to adjacent strands of the torus knots. In this article, we present an explicit formula for the Alexander polynomial of twisted torus knots. Our approach utilizes a presentation of the knot group of twisted torus knots combined with Fox's free differential calculus. As applications, we provide a lower bound for the genus of certain families of twisted torus knots and identify families of twisted torus knots that are not $L$-space knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13003 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Alexander polynomial of twisted torus knots Adnan Park, Kyungbae Geometric Topology 57K10, 57K14 Twisted torus knots are a generalization of torus knots, obtained by introducing additional full twists to adjacent strands of the torus knots. In this article, we present an explicit formula for the Alexander polynomial of twisted torus knots. Our approach utilizes a presentation of the knot group of twisted torus knots combined with Fox's free differential calculus. As applications, we provide a lower bound for the genus of certain families of twisted torus knots and identify families of twisted torus knots that are not $L$-space knots. |
| title | The Alexander polynomial of twisted torus knots |
| topic | Geometric Topology 57K10, 57K14 |
| url | https://arxiv.org/abs/2411.13003 |