Non-complex cobordisms between quasipositive knots
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908730915815424 |
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| author | Borodzik, Maciej Truöl, Paula |
| author_facet | Borodzik, Maciej Truöl, Paula |
| contents | We show that for every genus $g \geq 0$, there exist quasipositive knots $K_0^g$ and $K_1^g$ such that there is a cobordism of genus $g=|g_4(K_1^g)-g_4(K_0^g)|$ between $K_0^g$ and $K_1^g$, but there is no ribbon cobordism of genus $g$ in either direction and thus no complex cobordism between these two knots. This gives a negative answer to a question posed by Feller in 2016. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04894 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-complex cobordisms between quasipositive knots Borodzik, Maciej Truöl, Paula Geometric Topology 57K10 (Primary) 14H50 (Secondary) We show that for every genus $g \geq 0$, there exist quasipositive knots $K_0^g$ and $K_1^g$ such that there is a cobordism of genus $g=|g_4(K_1^g)-g_4(K_0^g)|$ between $K_0^g$ and $K_1^g$, but there is no ribbon cobordism of genus $g$ in either direction and thus no complex cobordism between these two knots. This gives a negative answer to a question posed by Feller in 2016. |
| title | Non-complex cobordisms between quasipositive knots |
| topic | Geometric Topology 57K10 (Primary) 14H50 (Secondary) |
| url | https://arxiv.org/abs/2504.04894 |