Combinatorial conditions for directed collapsing (Q2080092)

This paper studies a directed version of collapsing in directed Euclidian cubical complexes called link-preserving directed collapse (LPDC). The direction of the space is taken into account by requiring that the past links of vertices remain homotopy equivalent after collapsing. In the directed setting, topological properties -- in particular, properties of spaces of directed paths -- are not always preserved. In this paper, the authors give computationally simple conditions for preserving the topology of past links. Furthermore, they give conditions for when LPDC preserves the contractability and connectedness of spaces of directed paths. A lot of illustrative examples are also provided. For the entire collection see [Zbl 1487.55002].