Canonical stratifications along bisheaves
Algebraic Topology
2020-07-13 v2
Abstract
A theory of bisheaves has been recently introduced to measure the homological stability of fibers of maps to manifolds. A bisheaf over a topological space is a triple consisting of a sheaf, a cosheaf, and compatible maps from the stalks of the sheaf to the stalks of the cosheaf. In this note we describe how, given a bisheaf constructible (i.e., locally constant) with respect to a triangulation of its underlying space, one can explicitly determine the coarsest stratification of that space for which the bisheaf remains constructible.
Cite
@article{arxiv.1812.05593,
title = {Canonical stratifications along bisheaves},
author = {Vidit Nanda and Amit Patel},
journal= {arXiv preprint arXiv:1812.05593},
year = {2020}
}
Comments
10 pages; this is the Final Version which appeared in the Proceedings of the 2018 Abel Symposium on Topological Data Analysis