The next-to-top term in knot Floer homology

IF 1 2区数学 Q1 MATHEMATICS Quantum Topology Pub Date : 2021-04-29 DOI:10.4171/qt/174

Yi Ni

引用次数: 2

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 \[\mathrm{rank}\widehat{HFK}(Z,K,[F],g-1)\ge\mathrm{rank}\widehat{HFK}(Z,K,[F],g).\]

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结花同源性的下一个最上面的术语

设$K$是具有$b_1(Z)\le1$的广义l空间$Z$中的一个零同源结。设$F$为$K$的塞弗特曲面，其属为$g$。我们表明，如果在单个$\mathbb Z/2\mathbb Z$—分级中支持$\widehat{HFK}(Z,K,[F],g)$，那么 \[\mathrm{rank}\widehat{HFK}(Z,K,[F],g-1)\ge\mathrm{rank}\widehat{HFK}(Z,K,[F],g).\]

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.