A note on alternating knots in handlebodies
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915761299128320 |
|---|---|
| author | Buchanan, Lizzie Shah, Tanushree |
| author_facet | Buchanan, Lizzie Shah, Tanushree |
| contents | We establish a Kauffman-Murasugi-Thistlethwaite-type theorem for alternating knots in a solid torus. Specifically, we show that any dotted-reduced alternating diagram of a knot in a handlebody realizes the minimal crossing number, and that any two such diagrams of the same knot have identical writhe. The proof relies on a generalization of the Jones polynomial to the setting of handlebodies. A stronger version of this result was already proved by Boden, Karimi, and Sikora using a different generalized Jones polynomial; therefore, this text largely expands on one of the main proof tools. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21962 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on alternating knots in handlebodies Buchanan, Lizzie Shah, Tanushree Geometric Topology We establish a Kauffman-Murasugi-Thistlethwaite-type theorem for alternating knots in a solid torus. Specifically, we show that any dotted-reduced alternating diagram of a knot in a handlebody realizes the minimal crossing number, and that any two such diagrams of the same knot have identical writhe. The proof relies on a generalization of the Jones polynomial to the setting of handlebodies. A stronger version of this result was already proved by Boden, Karimi, and Sikora using a different generalized Jones polynomial; therefore, this text largely expands on one of the main proof tools. |
| title | A note on alternating knots in handlebodies |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2601.21962 |