Region colorings of surfaces in 4-space
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917992543027200 |
|---|---|
| author | Aranda, Román Crawford, Noah Maas, Andrew Marienau, Nicole Pearce, Erica Sarreal, Renzo Schutte, Savannah Sterns, Ransom Woods, Eric |
| author_facet | Aranda, Román Crawford, Noah Maas, Andrew Marienau, Nicole Pearce, Erica Sarreal, Renzo Schutte, Savannah Sterns, Ransom Woods, Eric |
| contents | Niebrzydowski introduced a theory of region colorings for surface links. In this paper, we translate the coloring invariant to the context of triplane diagrams and movies of knots. We provide inequalities between the number of region colorings and topological quantities of $F$, such as the number of saddles in a movie and the bridge index of a triplane diagram of $F$. As an application, we show that Yoshikawa's 2-knots $9_1$ and $10_2$ are non-invertible; that is $F\not=-F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14770 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Region colorings of surfaces in 4-space Aranda, Román Crawford, Noah Maas, Andrew Marienau, Nicole Pearce, Erica Sarreal, Renzo Schutte, Savannah Sterns, Ransom Woods, Eric Geometric Topology 57Q45 Niebrzydowski introduced a theory of region colorings for surface links. In this paper, we translate the coloring invariant to the context of triplane diagrams and movies of knots. We provide inequalities between the number of region colorings and topological quantities of $F$, such as the number of saddles in a movie and the bridge index of a triplane diagram of $F$. As an application, we show that Yoshikawa's 2-knots $9_1$ and $10_2$ are non-invertible; that is $F\not=-F$. |
| title | Region colorings of surfaces in 4-space |
| topic | Geometric Topology 57Q45 |
| url | https://arxiv.org/abs/2504.14770 |