Grid homology for singular links in lens space and a resolution cube
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913761852391424 |
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| author | Xiao, Yonghan |
| author_facet | Xiao, Yonghan |
| contents | In this paper, we define grid homologies for singular links in lens spaces and use them to construct a resolution cube for knot Floer homology of regular links in lens spaces. The results will first be proved over $\mathbb{Z}/2\mathbb{Z}$ and then over $\mathbb{Z}$ with the help of sign assignments. We will also identify the signed grid homology and classical knot Floer homology over $\mathbb{Z}$ for regular links in lens spaces, illustrating the fact that our resolution cube is genuinely one for knot Floer homology. The main advancement in the paper is that we give a complete description of singular knot theory in lens spaces which was only defined in $S^3$ previously and we construct a signed combinatorial resolution cube for knot Floer homology in lens spaces which may be powerful in relating $HFK^\circ$ to other link homology theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Grid homology for singular links in lens space and a resolution cube Xiao, Yonghan Geometric Topology 57K18 In this paper, we define grid homologies for singular links in lens spaces and use them to construct a resolution cube for knot Floer homology of regular links in lens spaces. The results will first be proved over $\mathbb{Z}/2\mathbb{Z}$ and then over $\mathbb{Z}$ with the help of sign assignments. We will also identify the signed grid homology and classical knot Floer homology over $\mathbb{Z}$ for regular links in lens spaces, illustrating the fact that our resolution cube is genuinely one for knot Floer homology. The main advancement in the paper is that we give a complete description of singular knot theory in lens spaces which was only defined in $S^3$ previously and we construct a signed combinatorial resolution cube for knot Floer homology in lens spaces which may be powerful in relating $HFK^\circ$ to other link homology theories. |
| title | Grid homology for singular links in lens space and a resolution cube |
| topic | Geometric Topology 57K18 |
| url | https://arxiv.org/abs/2501.03579 |