Stratifications and sheaves on the Ran space
Lazovskis, Jānis
arXiv, 1810.12358 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2018-10-29
Classification:  Mathematics - Algebraic Topology,  55U10, 57N80, 18A25, 55R80 
@article{1810.12358,
     author = {Lazovskis, J\=anis},
     title = {Stratifications and sheaves on the Ran space},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1810.12358}
}

Lazovskis, Jānis. Stratifications and sheaves on the Ran space. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1810.12358/