We construct a product on the Floer complex associated to a pair of Lagrangian cobordisms. More precisely, given three exact pairwise transverse Lagrangian cobordisms in the symplectization of a contact manifold, we define a map $\mathfrak{m}_2$ by a count of rigid pseudoholomorphic disks with boundary on the cobordisms and having punctures asymptotic to intersection points and Reeb chords of the negative Legendrian ends of the cobordisms. More generally, to a $(d + 1)$-tuple of exact transverse Lagrangian cobordisms we associate a map md such that the family $(\mathfrak{m}_d)_{d \geq 1}$ are maps satisfying the $A_\infty$ equations. Finally, we extend the Ekholm-Seidel isomorphism to an $A_\infty$-morphism, giving in particular that it is a ring isomorphism.

中文翻译：

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Floer理论中拉格朗日哥氏体的产品结构

我们在Floer复杂物上构建了与一对Lagrangian cobordisms相关的产品。更精确地讲，给定三个精确的成对的横向拉格朗日协方差，在接触流形的缩合中，我们定义了一个映射$ \ mathfrak {m} _2 $，其数量为刚性假全同性圆盘的边界，并且在点间渐近于交点和利勃勒弦的负传奇式末端的和弦。更一般而言，对于精确的横向拉格朗日肋章鱼的$（d + 1）$元组，我们将地图md关联为使得$（\ mathfrak {m} _d）_ {d \ geq 1} $家庭是满足$的地图A_ \ infty $方程。最后，我们将Ekholm-Seidel同构扩展为$ A_ \ infty $同构，尤其是给出它是一个环同构。