In this paper, we study a simplicial complex on the elements of the Tamari lattice in types A and B called the canonical join complex. The canonical join representation of an element w in a lattice L is the unique lowest expression ⋁A for w, when such an expression exists. We say that the set A is a canonical join representation. The collection of all such subsets has the structure of an abstract simplicial complex called the canonical join complex of L. We realize the canonical join complex of the Tamari lattice as a complex of noncrossing arc diagrams, give a shelling order on its facets, and show that it is homotopy equivalent to a wedge of Catalan-many spheres.

在本文中，我们研究了A和B型Tamari晶格元素上的简单复形，称为规范连接复形。规范加入的元素的表示瓦特为格子大号是唯一的最低表情⋁甲用于瓦特，当这样的表达存在。我们说集合A是规范的联接表示。所有这些子集的集合都具有称为L的规范连接复杂度的抽象简单复杂度的结构。我们将Tamari格的规范连接复杂体理解为非交叉弧图的复杂体，在其刻面上给出了脱壳顺序，并表明它是同构的，等效于加泰罗尼亚-许多球体的楔形。