Every non-trivial knot group is fully residually perfect
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_ | 1866909588991770624 |
|---|---|
| author | Ito, Tetsuya Motegi, Kimihiko Teragaito, Masakazu |
| author_facet | Ito, Tetsuya Motegi, Kimihiko Teragaito, Masakazu |
| contents | Given a class $\mathcal{P}$ of groups we say that a group $G$ is fully residually $\mathcal{P}$ if for any finite subset $F$ of $G$, there exists an epimorphism from $G$ to a group in $\mathcal{P}$ which is injective on $F$. It is known that any non-trivial knot group is fully residually finite. For hyperbolic knots, its knot group is fully residually closed hyperbolic $3$--manifold group, and fully residually simple. In this article, we show that every non-trivial knot group is fully residually perfect, closed $3$--manifold group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Every non-trivial knot group is fully residually perfect Ito, Tetsuya Motegi, Kimihiko Teragaito, Masakazu Geometric Topology Group Theory fundamental group, knot group, fully residually perfect, Dehn filling, graph of groups, small cancellation Given a class $\mathcal{P}$ of groups we say that a group $G$ is fully residually $\mathcal{P}$ if for any finite subset $F$ of $G$, there exists an epimorphism from $G$ to a group in $\mathcal{P}$ which is injective on $F$. It is known that any non-trivial knot group is fully residually finite. For hyperbolic knots, its knot group is fully residually closed hyperbolic $3$--manifold group, and fully residually simple. In this article, we show that every non-trivial knot group is fully residually perfect, closed $3$--manifold group. |
| title | Every non-trivial knot group is fully residually perfect |
| topic | Geometric Topology Group Theory fundamental group, knot group, fully residually perfect, Dehn filling, graph of groups, small cancellation |
| url | https://arxiv.org/abs/2504.16345 |