Colored knot Floer homology: structures and examples
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918132692549632 |
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| author | Alishahi, Akram Gorsky, Eugene Liu, Beibei |
| author_facet | Alishahi, Akram Gorsky, Eugene Liu, Beibei |
| contents | Inspired by the $S^n$ colored version of Khovanov and Khovanov-Rozansky homology, we define a colored version of knot Floer homology by studying the colimit of a directed system of link Floer homology with infinite full twists. Specifically, our $n$-colored knot Floer homology of a knot $K$ is then defined as the colimit of the link Floer homology of $(n, mn)$-cables of $K$ by fixing $n$ and letting $m$ goes to infinity. We show that the colimit of the infinite full twists is a module over the colored knot Floer homology of the unknot. In addition, we give an explicit description of colored Heegaard Floer homology for L-space knots, and maps for colored knot Floer homology of crossing changes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Colored knot Floer homology: structures and examples Alishahi, Akram Gorsky, Eugene Liu, Beibei Geometric Topology Inspired by the $S^n$ colored version of Khovanov and Khovanov-Rozansky homology, we define a colored version of knot Floer homology by studying the colimit of a directed system of link Floer homology with infinite full twists. Specifically, our $n$-colored knot Floer homology of a knot $K$ is then defined as the colimit of the link Floer homology of $(n, mn)$-cables of $K$ by fixing $n$ and letting $m$ goes to infinity. We show that the colimit of the infinite full twists is a module over the colored knot Floer homology of the unknot. In addition, we give an explicit description of colored Heegaard Floer homology for L-space knots, and maps for colored knot Floer homology of crossing changes. |
| title | Colored knot Floer homology: structures and examples |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2508.21776 |