Local cohomology and stratification

Author: 

Nanda, V

Publication Date: 

13 June 2019

Journal: 

Foundations of Computational Mathematics

Last Updated: 

2020-10-06T13:28:38.457+01:00

Volume: 

20

DOI: 

10.1007/s10208-019-09424-0

page: 

195-222

abstract: 

We outline an algorithm to recover the canonical (or, coarsest) stratification of a given finite-dimensional regular CW complex into cohomology manifolds, each of which is a union of cells. The construction proceeds by iteratively localizing the poset of cells about a family of subposets; these subposets are in turn determined by a collection of cosheaves which capture variations in cohomology of cellular neighborhoods across the underlying complex. The result is a nested sequence of categories, each containing all the cells as its set of objects, with the property that two cells are isomorphic in the last category if and only if they lie in the same canonical stratum. The entire process is amenable to efficient distributed computation.

Symplectic id: 

999297

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article