Slice genus bound in $DTS^2$ from $s$-invariant
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910748165275648 |
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| author | Ren, Qiuyu |
| author_facet | Ren, Qiuyu |
| contents | We prove a recent conjecture of Manolescu-Willis which states that the $s$-invariant of a knot in $\mathbb{RP}^3$ (as defined by them) gives a lower bound on its null-homologous slice genus in the unit disk bundle of $TS^2$. We also conjecture a lower bound in the more general case where the slice surface is not necessarily null-homologous, and give its proof in some special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17816 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Slice genus bound in $DTS^2$ from $s$-invariant Ren, Qiuyu Geometric Topology Quantum Algebra 57K18 (Primary) 57K10, 57K40 (Secondary) We prove a recent conjecture of Manolescu-Willis which states that the $s$-invariant of a knot in $\mathbb{RP}^3$ (as defined by them) gives a lower bound on its null-homologous slice genus in the unit disk bundle of $TS^2$. We also conjecture a lower bound in the more general case where the slice surface is not necessarily null-homologous, and give its proof in some special cases. |
| title | Slice genus bound in $DTS^2$ from $s$-invariant |
| topic | Geometric Topology Quantum Algebra 57K18 (Primary) 57K10, 57K40 (Secondary) |
| url | https://arxiv.org/abs/2306.17816 |