Year: 2024
Type: article
Abstract: We discuss the Mayer-Vietoris spectral sequence as an invariant in the context of persistent homology.In particular, we introduce the notion of "-acyclic carriers and "-acyclic equivalences between filtered regular CW-complexes and study stability conditions for the associated spectral sequences.We also look at the Mayer-Vietoris blowup complex and the geometric realization, finding stability properties under compatible noise; as a result we prove a version of an approximate nerve theorem.Adapting work by Serre, we find conditions under which "-interleavings exist between the spectral sequences associated to two different covers.
Source: Algebraic & Geometric Topology
Authors: Álvaro Torras-Casas, Ulrich Pennig
Institution: Cardiff University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405637161