Talk Title: Künneth Formulae in Persistent Homology
Event: AMS Contributed Paper Session on General Topology, Algebraic Topology, and Topology of Manifolds
Where: Joint Mathematics Meetings, Baltimore
Date: January 17, 2019
Abstract: The classical Kunneth formula in homological algebra provides a relationship between the homology of a product space and those of its factors. In this talk, we will give similar results for persistent homology. That is, we will give relationships between barcodes of two different notions of product filtrations and that of their factor filtered spaces. We also present two applications: one gives faster algorithms for computing persistent homology in the setting of Vietoris-Rips complexes and the other gives barcodes for certain multiparameter persistence modules.