Stratifications and sheaves on the Ran space
Jānis Lazovskis · arXiv (Cornell University) · 2018
We describe poset stratifications of the product of the Ran space and the nonnegative real numbers, as a universal space for the \v Cech construction of simplicial complexes. This leads to a cosheaf valued in diagrams of simplicial complexes for which every restriction to $\{P\}\times \mathbf{R}_{\geqslant 0}$ recovers the persistent homology of the data set $P$. For the stratification, we describe a partial order on isomorphism classes of abstract simplicial complexes, which allows spaces stratified by them to have entrance paths uniquely interpreted as simplicial maps.