The next-to-top term in knot Floer homology

Yi Ni

The next-to-top term in knot Floer homology

Geometric Topology 2021-05-03 v1

Authors: Yi Ni

Abstract

Let $K$ be a null-homologous knot in a generalized L-space $Z$ with $b_1(Z)\le1$ . Let $F$ be a Seifert surface of $K$ with genus $g$ . We show that if $\widehat{HFK}(Z,K,[F],g)$ is supported in a single $\mathbb Z/2\mathbb Z$ --grading, then $\mathrm{rank}\widehat{HFK}(Z,K,[F],g-1)\ge\mathrm{rank}\widehat{HFK}(Z,K,[F],g).$

Keywords

knot floer homology null-homologous knot generalized l-space seifert surface rank inequality

Cite

@article{arxiv.2104.14687,
  title  = {The next-to-top term in knot Floer homology},
  author = {Yi Ni},
  journal= {arXiv preprint arXiv:2104.14687},
  year   = {2021}
}

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10 pages

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