2018/02/28 by Peter Bubenik, Tane Vergili · 1 citation
Mathematics · #math.AT #math.GN #msc:55N99 #msc:54A05 #msc:18A25
paper · pdf · doi:10.1007/s41468-018-0022-4
published as Journal of Applied and Computational Topology (2018) 2:233-269 · 32 pages, to appear in Journal of Applied and Computational Topology
arxiv created 2018/10/25 · arxiv updated 2019/12/12
Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules, including many of those that have been previously studied, and describe the relationships between them. In the cases where these classes are sets, interleaving distance induces a topology. We undertake a systematic study the resulting topological spaces and their basic topological properties.