Pairs of knot invariants
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929462460809216 |
|---|---|
| author | Taniyama, Kouki |
| author_facet | Taniyama, Kouki |
| contents | Let $α$ be a map from the set of all knot types ${\mathcal K}$ to a set $X$. Let $β$ be a map from ${\mathcal K}$ to a set $Y$. We define the relation between $α$ and $β$ to be the image of a map $(α,β)$ from ${\mathcal K}$ to $X\times Y$ sending an element $K$ of ${\mathcal K}$ to $(α(K),β(K))$. We determine the relations between $α$ and $β$ for certain $α$ and $β$ such as crossing number, unknotting number, bridge number, braid index, genus and canonical genus. This is a study of geography problem in knot theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09283 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pairs of knot invariants Taniyama, Kouki Geometric Topology 57K10 Let $α$ be a map from the set of all knot types ${\mathcal K}$ to a set $X$. Let $β$ be a map from ${\mathcal K}$ to a set $Y$. We define the relation between $α$ and $β$ to be the image of a map $(α,β)$ from ${\mathcal K}$ to $X\times Y$ sending an element $K$ of ${\mathcal K}$ to $(α(K),β(K))$. We determine the relations between $α$ and $β$ for certain $α$ and $β$ such as crossing number, unknotting number, bridge number, braid index, genus and canonical genus. This is a study of geography problem in knot theory. |
| title | Pairs of knot invariants |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2404.09283 |