L-space satellite operators and knot Floer homology
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912147854852096 |
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| author | Chen, Daren Zemke, Ian Zhou, Hugo |
| author_facet | Chen, Daren Zemke, Ian Zhou, Hugo |
| contents | We consider satellite operators where the corresponding 2-component link is an L-space link. This family includes many commonly studied satellite operators, including cabling operators, the Whitehead operator, and a family of Mazur operators. We give a formula which computes the knot Floer complex of a satellite of $K$ in terms of the knot Floer complex of $K$. Our main tools are the Heegaard Floer Dehn surgery formulas and their refinements. A key step in our computation is a proof that 2-component L-space links have formal knot Floer complexes. We use this to show that the link Floer complexes of 2-component L-space links are determined by their multivariable Alexander polynomials. We implement our satellite formula in Python code, which we also make available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | L-space satellite operators and knot Floer homology Chen, Daren Zemke, Ian Zhou, Hugo Geometric Topology 57K18, 57K10, 57K14 We consider satellite operators where the corresponding 2-component link is an L-space link. This family includes many commonly studied satellite operators, including cabling operators, the Whitehead operator, and a family of Mazur operators. We give a formula which computes the knot Floer complex of a satellite of $K$ in terms of the knot Floer complex of $K$. Our main tools are the Heegaard Floer Dehn surgery formulas and their refinements. A key step in our computation is a proof that 2-component L-space links have formal knot Floer complexes. We use this to show that the link Floer complexes of 2-component L-space links are determined by their multivariable Alexander polynomials. We implement our satellite formula in Python code, which we also make available. |
| title | L-space satellite operators and knot Floer homology |
| topic | Geometric Topology 57K18, 57K10, 57K14 |
| url | https://arxiv.org/abs/2412.05755 |