论文标题
Plabic Links，Quivers和skein关系
Plabic links, quivers, and skein relations
论文作者
论文摘要
我们研究群集代数不变性和链接不变性之间的关系。 首先，我们表明源自链链链路的几种构造（置换链接，理查森链接，网格图链接，Plabic Graph Links）会产生同位素链接。对于由凹形曲线产生的排列子类，我们还提供了具有相应的Coxeter链接的同位素。 其次，我们将点计数多项式与任意的局部无环颤动相关联。我们猜想了Plabic图链接的Homfly多项式的顶部$ a $程度系数与其平面双颤动的点数多项式之间的平等。我们证明了叶片复发图形的猜想，其中包括降低的牙齿图和特殊情况。
We study relations between cluster algebra invariants and link invariants. First, we show that several constructions of positroid links (permutation links, Richardson links, grid diagram links, plabic graph links) give rise to isotopic links. For a subclass of permutations arising from concave curves, we also provide isotopies with the corresponding Coxeter links. Second, we associate a point count polynomial to an arbitrary locally acyclic quiver. We conjecture an equality between the top $a$-degree coefficient of the HOMFLY polynomial of a plabic graph link and the point count polynomial of its planar dual quiver. We prove this conjecture for leaf recurrent plabic graphs, which includes reduced plabic graphs and plabic fences as special cases.
