Contribution to Book
Combinatorial Conditions for Directed Collapsing
Research in Computational Topology 2
(2022)
Abstract
While collapsibility of CW complexes dates back to the 1930s, collapsibility of directed Euclidean cubical complexes has not been well studied to date. The classical definition of collapsibility involves certain conditions on pairs of cells 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 the undirected setting, pairs of cells are removed that create a deformation retract. In the directed setting, topological properties—in particular, properties of spaces of directed paths—are not always preserved. In this paper, we give computationally simple conditions for preserving the topology of past links. Furthermore, we give conditions for when link-preserving directed collapses preserve the contractability and connectedness of spaces of directed paths. Throughout, we provide illustrative examples.
Disciplines
Publication Date
May, 2022
Editor
Ellen Gasparovic, Vanessa Robins, Katharine Turner
Publisher
Springer
Series
Association for Women in Mathematics Series
ISBN
978-3-030-95519-9
DOI
10.1007/978-3-030-95519-9_7
Citation Information
Robin Belton, Robyn Brooks, Stefania Ebli, Lisbeth Fajstrup, et al.. "Combinatorial Conditions for Directed Collapsing" 1Research in Computational Topology 2 Vol. 30 (2022) p. 167 - 189 Available at: http://works.bepress.com/elizabeth-vidaurre/1/