Constructing knots with low rational genera
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912719628664832 |
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| author | McDonald, Clayton Miller, Allison N. |
| author_facet | McDonald, Clayton Miller, Allison N. |
| contents | We give a flexible construction for knots in the 3-sphere that bound surfaces of unexpectedly low genus in punctured open books on 3-manifolds. We use this construction to give the first examples of knots whose genus differs in different $\mathbb{Z}/2\mathbb{Z}$ homology balls. We also establish that every knot bounds a M{ö}bius band in a rational homology ball, and that there are knots whose genus in $T^4$ and $B^4$ differ arbitrarily. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing knots with low rational genera McDonald, Clayton Miller, Allison N. Geometric Topology 57K10 We give a flexible construction for knots in the 3-sphere that bound surfaces of unexpectedly low genus in punctured open books on 3-manifolds. We use this construction to give the first examples of knots whose genus differs in different $\mathbb{Z}/2\mathbb{Z}$ homology balls. We also establish that every knot bounds a M{ö}bius band in a rational homology ball, and that there are knots whose genus in $T^4$ and $B^4$ differ arbitrarily. |
| title | Constructing knots with low rational genera |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2511.15900 |