Skein theory for the Links-Gould polynomial
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917319865794560 |
|---|---|
| author | Garoufalidis, Stavros Harper, Matthew Kashaev, Rinat Kohli, Ben-Michael Song, Jiebo Tahar, Guillaume |
| author_facet | Garoufalidis, Stavros Harper, Matthew Kashaev, Rinat Kohli, Ben-Michael Song, Jiebo Tahar, Guillaume |
| contents | Building further on work of Marin and Wagner, we give a cubic braid-type skein theory of the Links--Gould polynomial invariant of oriented links and prove that it can be used to evaluate any oriented link, adding this polynomial to the list of polynomial invariants that can be computed by skein theory. As a consequence, we prove that this skein theory is also shared by the $V_1$-polynomial defined by two of the authors, deducing the equality of the two link polynomials. This implies specialization properties of the $V_1$-polynomial to the Alexander polynomial and to the $\mathrm{ADO}_3$-invariant, the fact that it is a Vassiliev power series invariant, as well as a Seifert genus bound for knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19251 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Skein theory for the Links-Gould polynomial Garoufalidis, Stavros Harper, Matthew Kashaev, Rinat Kohli, Ben-Michael Song, Jiebo Tahar, Guillaume Geometric Topology Quantum Algebra 57K14 (Primary) 57K16 (Secondary) Building further on work of Marin and Wagner, we give a cubic braid-type skein theory of the Links--Gould polynomial invariant of oriented links and prove that it can be used to evaluate any oriented link, adding this polynomial to the list of polynomial invariants that can be computed by skein theory. As a consequence, we prove that this skein theory is also shared by the $V_1$-polynomial defined by two of the authors, deducing the equality of the two link polynomials. This implies specialization properties of the $V_1$-polynomial to the Alexander polynomial and to the $\mathrm{ADO}_3$-invariant, the fact that it is a Vassiliev power series invariant, as well as a Seifert genus bound for knots. |
| title | Skein theory for the Links-Gould polynomial |
| topic | Geometric Topology Quantum Algebra 57K14 (Primary) 57K16 (Secondary) |
| url | https://arxiv.org/abs/2505.19251 |