Self and mixed delta-moves on algebraically split links
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910525877649408 |
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| author | Bosman, Anthony Garcia, Devin Goode, Justyce Kas-Danouche, Yamil Smith, Davielle |
| author_facet | Bosman, Anthony Garcia, Devin Goode, Justyce Kas-Danouche, Yamil Smith, Davielle |
| contents | A delta-move is a local move on a link diagram. The delta-Gordian distance between links measures the minimum number of delta-moves needed to move between link diagrams. A self delta-move only involves a single component of a link whereas a mixed delta-move involves multiple (2 or 3) components. We prove that two links are mixed delta-equivalent precisely when they have the same pairwise linking number and same components; we also give a number of results on how (mixed/self) delta-moves relate to classical link invariants including the Arf invariant and crossing number. This allows us to produce a graph showing links related by a self delta-move for algebraically split links with up to 9-crossings. For these links we also introduce and calculate the delta-splitting number and mixed delta-splitting number, that is, the minimum number of delta-moves needed to separate the components of the link. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self and mixed delta-moves on algebraically split links Bosman, Anthony Garcia, Devin Goode, Justyce Kas-Danouche, Yamil Smith, Davielle Geometric Topology A delta-move is a local move on a link diagram. The delta-Gordian distance between links measures the minimum number of delta-moves needed to move between link diagrams. A self delta-move only involves a single component of a link whereas a mixed delta-move involves multiple (2 or 3) components. We prove that two links are mixed delta-equivalent precisely when they have the same pairwise linking number and same components; we also give a number of results on how (mixed/self) delta-moves relate to classical link invariants including the Arf invariant and crossing number. This allows us to produce a graph showing links related by a self delta-move for algebraically split links with up to 9-crossings. For these links we also introduce and calculate the delta-splitting number and mixed delta-splitting number, that is, the minimum number of delta-moves needed to separate the components of the link. |
| title | Self and mixed delta-moves on algebraically split links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2401.07372 |