The purpose of this article is to study directed collapsibility of directed Euclidean cubical complexes. One application of this is in the nontrivial task of verifying the execution of concurrent programs. The classical definition of collapsibility involves certain conditions on a pair of cubes of the complex. The direction of the space can be taken into account by requiring that the past links of vertices remain homotopy equivalent after collapsing. We call this type of collapse a link-preserving directed collapse. In this paper, we give combinatorially equivalent conditions for preserving the topology of the links, allowing for the implementation of an algorithm for collapsing a directed Euclidean cubical complex. Furthermore, we give conditions for when link-preserving directed collapses preserve the contractability and connectedness of directed path spaces, as well as examples when link-preserving directed collapses do not preserve the number of connected components of the path space between the minimum and a given vertex.

翻译：本条的目的是研究定向欧洲立方体结构的定向折叠性,其中一项应用是用于核查并行程序执行情况的非三重任务。典型的折叠性定义涉及综合体一对立方体的某些条件。空间的方向可以通过要求过去脊椎的连接在崩溃后保持同质性来加以考虑。我们把这种类型的折叠称为保留链接的定向折叠。在本文中,我们给保留链接的表层提供了相近的条件,允许实施一个算法以瓦解指定的欧洲立方体结构。此外,我们还为保持连接的定向折叠性保持定向路径空间的合合合性和连接性提供了条件,并举例说,保留链接的定向折叠不保留最小和给定的顶端之间的路径空间连接组成部分数目。