The Non-Orientable Four-Ball Genus of a New Infinite Family of Torus Knots
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916869199364096 |
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| author | Sinha, Shreya |
| author_facet | Sinha, Shreya |
| contents | We extend previous work by using a combination of band surgeries and known bounds to compute $γ_4(T_{4n, (2n\pm1)^2 + 4n-2}) = 2n-1$ for all $n \geq 1$. We further generalize this result by showing that $γ_4(T_{4n + 2k, n(4n + 2k) - 1}) = γ_4(T_{4n + 2k, (n+2)(4n + 2k) - 1}) = 2n-1 + k$ for all $n \geq 1$ and $k \geq 0$. All knots in this family are counterexamples to Batson's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Non-Orientable Four-Ball Genus of a New Infinite Family of Torus Knots Sinha, Shreya Geometric Topology Algebraic Topology We extend previous work by using a combination of band surgeries and known bounds to compute $γ_4(T_{4n, (2n\pm1)^2 + 4n-2}) = 2n-1$ for all $n \geq 1$. We further generalize this result by showing that $γ_4(T_{4n + 2k, n(4n + 2k) - 1}) = γ_4(T_{4n + 2k, (n+2)(4n + 2k) - 1}) = 2n-1 + k$ for all $n \geq 1$ and $k \geq 0$. All knots in this family are counterexamples to Batson's conjecture. |
| title | The Non-Orientable Four-Ball Genus of a New Infinite Family of Torus Knots |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2507.12606 |