Local cohomology and stratification
Every finite regular CW complex is, ipso facto, a stratified space when filtered by skeleta. In this talk, I will outline a method to discover the canonical (i.e., coarsest possible) stratification into manifolds of such a complex that is compatible with its underlying cell structure. The construction proceeds by first localizing and then resolving a sequence of cosheaves which capture local cohomology at every cell. The result is a sequence of categories whose limit recovers the desired strata via its (isomorphism classes of) objects. As a bonus, the entire process is algorithmic and amenable to efficient computation.
IPAB seminar - 05/07/2017