结调和不变量的组合描述

Subhankar Dey, Hakan Doga
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引用次数: 0

摘要

本文给出了Hom在\cite{hom2011knot}中定义的一致性不变量$\varepsilon$的组合描述,并利用网格同调技术证明了该不变量的一些性质。我们还计算了$(p,q)$环面结的$\varepsilon$,并证明了$\varepsilon(\mathbb{G}_+)=1$如果$\mathbb{G}_+$是一个正编织的网格图。此外,我们展示了$\varepsilon$在负环面结的$(p,q)$ -布线下的行为。
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A Combinatorial Description of the Knot Concordance Invariant Epsilon
In this paper, we give a combinatorial description of the concordance invariant $\varepsilon$ defined by Hom in \cite{hom2011knot}, prove some properties of this invariant using grid homology techniques. We also compute $\varepsilon$ of $(p,q)$ torus knots and prove that $\varepsilon(\mathbb{G}_+)=1$ if $\mathbb{G}_+$ is a grid diagram for a positive braid. Furthermore, we show how $\varepsilon$ behaves under $(p,q)$-cabling of negative torus knots.
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