标题： 平面图的边界纽结代数变形 显示英文标题

标题： Planar graphs deformations of bordered knot algebras

摘要： 在之前的一篇论文中，我们引入了“边界纽结代数”，它们是由一对整数(m,k)索引的分次代数。在后续的一篇论文中，我们引入了一个双参数的微分分次代数族，“pong代数”，并将其同调与边界纽结代数联系起来，并表征了同调上的诱导A-无穷结构。本文的目的是为边界纽结代数上的这种A-无穷结构提供一个显式的、组合的模型，以及在k=1的情况下，对该结构的进一步加权变形。 显示英文摘要

摘要： In an earlier paper, we introduced ``bordered knot algebras'', which are graded algebras indexed by a pair of integers (m,k). In a subsequent paper, we introduced a two-parameter family of differential graded algebra, the ``pong algebras'', and identified their homology with the bordered knot algebras, and characterized the induced A-infinity structure on the homology. The aim of the present paper is to give an explicit, combinatorial model for this A-infinity structure on the bordered knot algebras, and a further weighted deformation of this structure, in the case where k=1.