标题： 全扭转和纽结与箭图的稳定性 显示英文标题

标题： Full twists and stability of knots and quivers

摘要： 我们将纽结不变量在扭转一对弦下的稳定性与对称箭袋在解缠绕（或缠绕）操作下的稳定性联系起来。 从HOMFLY-PT的辫子关系出发，我们确认了在纽结上添加一个完整扭转时，$Sym^r$色HOMFLY-PT多项式的稳定增长。 另一方面，我们证明了对称箭袋在增加额外节点的箭袋进行解缠绕或缠绕时表现出类似的稳定增长；在某些情况下，这个增广箭袋捕捉了该序列中所有箭袋的动机Donaldson-Thomas不变量谱。 结合这两种稳定增长的形式，我们猜想对任何纽结进行一个完整扭转相当于对应增广箭袋的适当解缠绕或缠绕——这一陈述是基于纽结图直接定义纽结-箭袋对应关系的重要一步。 我们验证了该猜想对于所有扭结、$(2,2p+1)$环面纽结以及每个扭结区域中扭转数为奇数且交叉数不超过15的所有三叶形纽结。 显示英文摘要

摘要： We relate the stability of knot invariants under twisting a pair of strands to the stability of symmetric quivers under unlinking (or linking) operation. Starting from the HOMFLY-PT skein relations, we confirm the stable growth of $Sym^r$-coloured HOMFLY-PT polynomials under the addition of a~full twist to the knot. On the other hand, we show that symmetric quivers exhibit analogous stable growth under unlinking or linking of the quiver augmented with the extra node; in some cases this augmented quiver captures the spectrum of motivic Donaldson-Thomas invariants of all quivers in the sequence. Combining these two versions of the stable growth, we conjecture that performing a~full twist on any knot corresponds to appropriate unlinking or linking of the corresponding augmented quiver -- this statement is an important step towards a~direct definition of the knot-quiver correspondence based on the knot diagram. We confirm the conjecture for all twist knots, $(2,2p+1)$ torus knots, and all pretzel knots up to 15 crossings with an~odd number of twists in each twist region.