Jones Polynomials and their Zeros for a Family of Knots and Links
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917068452921344 |
|---|---|
| author | Chen, Yue Shrock, Robert |
| author_facet | Chen, Yue Shrock, Robert |
| contents | We calculate Jones polynomials $V(H_r,t)$ for a family of alternating knots and links $H_r$ with arbitrarily many crossings $r$, by computing the Tutte polynomials $T(G_+(H_r),x,y)$ for the associated graphs $G_+(H_r)$ and evaluating these with $x=-t$ and $y=-1/t$. Our method enables us to circumvent the generic feature that the computational complexity of $V(L_r,t)$ for a knot or link $L_r$ for generic $t$ grows exponentially rapidly with $r$. We also study the accumulation set of the zeros of these polynomials in the limit of infinitely many crossings, $r \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jones Polynomials and their Zeros for a Family of Knots and Links Chen, Yue Shrock, Robert Mathematical Physics Geometric Topology We calculate Jones polynomials $V(H_r,t)$ for a family of alternating knots and links $H_r$ with arbitrarily many crossings $r$, by computing the Tutte polynomials $T(G_+(H_r),x,y)$ for the associated graphs $G_+(H_r)$ and evaluating these with $x=-t$ and $y=-1/t$. Our method enables us to circumvent the generic feature that the computational complexity of $V(L_r,t)$ for a knot or link $L_r$ for generic $t$ grows exponentially rapidly with $r$. We also study the accumulation set of the zeros of these polynomials in the limit of infinitely many crossings, $r \to \infty$. |
| title | Jones Polynomials and their Zeros for a Family of Knots and Links |
| topic | Mathematical Physics Geometric Topology |
| url | https://arxiv.org/abs/2507.03680 |