论文标题
通用组合单纯形
The generic combinatorial simplex
论文作者
论文摘要
我们采用投射的fraïssé理论来定义“通用组合$ n $ - 简单”作为亲限的，简单的复合体，与单纯的三角形之间的简单定义选择图在规范上相关联。通用组合$ n $ -simplex是一个组合对象，可用于定义简单复合物的几何实现，而无需任何参考欧几里得空间。它还反映了其同质形态组的动力学特性，这些特性是有限组合学的。 作为对通用组合单纯形的研究的一部分，我们定义并证明了Fraïssé类的支配性闭合结果，并进一步发展了恒星移动和细胞图的理论。我们证明，选择地图的主导地位包含一类具有脸部的简单图，这些图是$ n $ simplex的每个面上的细胞，并包含在简单，脸部保护的近乎塑料的类别中。在Pl-Poincaré猜想下，这给出了选择的主导闭合的特征。
We employ projective Fraïssé theory to define the "generic combinatorial $n$-simplex" as the pro-finite, simplicial complex that is canonically associated with a family of simply defined selection maps between finite triangulations of the simplex. The generic combinatorial $n$-simplex is a combinatorial object that can be used to define the geometric realization of a simplicial complex without any reference to the Euclidean space. It also reflects dynamical properties of its homeomorphism group down to finite combinatorics. As part of our study of the generic combinatorial simplex, we define and prove results on domination closure for Fraïssé classes, and we develop further the theories of stellar moves and cellular maps. We prove that the domination closure of selection maps contains the class of face-preserving simplicial maps that are cellular on each face of the $n$-simplex and is contained in the class of simplicial, face-preserving near-homeomorphisms. Under the PL-Poincaré conjecture, this gives a characterization of the domination closure of selections.
