Title: Multi-cover skeins, quivers, and 3d $\mathcal{N}=2$ dualities Show Chinese title

Title: 多覆盖链环、箭头图和三维$\mathcal{N}=2$对偶性

Abstract: The relation between open topological strings and representation theory of symmetric quivers is explored beyond the original setting of the knot-quiver correspondence. Multiple cover generalizations of the skein relation for boundaries of holomorphic disks on a Lagrangian brane are observed to generate dual quiver descriptions of the geometry. Embedding into M-theory, a large class of dualities of 3d $\mathcal{N}=2$ theories associated to quivers is obtained. The multi-cover skein relation admits a compact formulation in terms of quantum torus algebras associated to the quiver and in this language the relations are similar to wall-crossing identities of Kontsevich and Soibelman. Show Chinese abstract

Abstract: 开放拓扑弦与对称箭图的表示理论之间的关系在原始的纽结-箭图对应设置之外被探索。 观察到全纯圆盘边界上的辫子关系的多重覆盖推广，可以生成几何的对偶箭图描述。 嵌入到M理论中，得到了与箭图相关的3d$\mathcal{N}=2$理论的一类大量对偶性。 多重覆盖辫子关系可以用与箭图相关的量子环面代数进行紧凑表述，在这种语言中，这些关系类似于Kontsevich和Soibelman的墙穿越恒等式。