The next-to-top term in knot Floer homology (Q2697607)
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scientific article; zbMATH DE number 7673857
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The next-to-top term in knot Floer homology |
scientific article; zbMATH DE number 7673857 |
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The next-to-top term in knot Floer homology (English)
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12 April 2023
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Summary: Let \(K\) be a null-homologous knot in a generalized L-space \(Z\) with \(b_1 (Z) \leq 1\). Let \(F\) be a Seifert surface of \(K\) with genus \(g\). We show that if \(\widehat{\mathrm{HFK}}(Z,K,[F],g)\) is supported in a single \(\mathbb{Z} / 2 \mathbb{Z}\)-grading, then \[ \operatorname{rank} \widehat{\mathrm{HFK}} (Z, K, [F], g - 1) \geq \operatorname{rank} \widehat{\mathrm{HFK}} (Z, K, [F], g). \]
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knot Floer homology
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next-to-top term
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