Algorithmic canonical stratifications of simplicial complexes

Abstract

We introduce a new algorithm for the structural analysis of finite abstract simplicial complexes based on local homology. Through an iterative and top-down procedure, our algorithm computes a stratification π of the poset P of simplices of a simplicial complex K, such that for each strata Pπ=i⊂P, Pπ=i is maximal among all open subposets U⊂Pπ=i‾ in its closure such that the restriction of the local Z-homology sheaf of Pπ=i‾ to U is locally constant. Passage to the localization of P dictated by π then attaches a canonical stratified homotopy type to K.