Diagonal Approximations on Finite Regular CW Complexes: Theory, Implementation, and Applications

Abstract

We describe an algorithm for recursively constructing diagonal approximations on finite regular CW-complexes where the closure of each cell can be explicitly collapsed to a point. The algorithm is based on the standard proof of the acyclic carrier theorem and is made constructive through the use of explicit contracting homotopies. We compare the algorithm’s output with existing diagonal approximations for the families of simplices, cubes, associahedra, and permutahedra