A note on knot Floer homology of satellite knots with (1,1)-patterns
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911209469509632 |
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| author | Shen, Weizhe |
| author_facet | Shen, Weizhe |
| contents | We prove that if $P$ is a $(1,1)$-pattern knot, the two inequalities $\dim \widehat{HFK} (P(K)) \geqslant \dim \widehat{HFK} (P(U))$ and $\dim \widehat{HFK} (P(K)) \geqslant \dim \widehat{HFK} (K)$ hold for the unknot $U\subset S^3$ and any companion knot $K\subset S^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01787 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A note on knot Floer homology of satellite knots with (1,1)-patterns Shen, Weizhe Geometric Topology 57K18, 57R58 We prove that if $P$ is a $(1,1)$-pattern knot, the two inequalities $\dim \widehat{HFK} (P(K)) \geqslant \dim \widehat{HFK} (P(U))$ and $\dim \widehat{HFK} (P(K)) \geqslant \dim \widehat{HFK} (K)$ hold for the unknot $U\subset S^3$ and any companion knot $K\subset S^3$. |
| title | A note on knot Floer homology of satellite knots with (1,1)-patterns |
| topic | Geometric Topology 57K18, 57R58 |
| url | https://arxiv.org/abs/2207.01787 |