Surgeries between lens spaces of type $L(n,1)$ and the Heegaard Floer $d$-invariant
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908299092295680 |
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| author | Wu, Zhongtao Yang, Jingling |
| author_facet | Wu, Zhongtao Yang, Jingling |
| contents | We establish a $d$-invariant surgery formula for $L$-space knots that provides an effective tool for studying surgeries between lens spaces. Using this formula, we classify distance one surgeries between lens spaces of the form $L(n,1)$. This classification has direct applications to band surgeries between torus links $T(2,n)$, with connections to DNA topology. In particular, we show that chirally cosmetic banding of torus links can possibly occur only when $n=1,5,9$ or $10$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Surgeries between lens spaces of type $L(n,1)$ and the Heegaard Floer $d$-invariant Wu, Zhongtao Yang, Jingling Geometric Topology 57K18, 57K10, 57K31, 57R58, 57M12 We establish a $d$-invariant surgery formula for $L$-space knots that provides an effective tool for studying surgeries between lens spaces. Using this formula, we classify distance one surgeries between lens spaces of the form $L(n,1)$. This classification has direct applications to band surgeries between torus links $T(2,n)$, with connections to DNA topology. In particular, we show that chirally cosmetic banding of torus links can possibly occur only when $n=1,5,9$ or $10$. |
| title | Surgeries between lens spaces of type $L(n,1)$ and the Heegaard Floer $d$-invariant |
| topic | Geometric Topology 57K18, 57K10, 57K31, 57R58, 57M12 |
| url | https://arxiv.org/abs/2504.02325 |