English

Topological Correlation

Algebraic Topology 2025-06-23 v1 Computational Geometry

Abstract

We introduce two novel concepts, topological difference and topological correlation, that offer a new perspective on the discriminative power of multiparameter persistence. The former quantifies the discrepancy between multiparameter and monoparameter persistence, while the other leverages this gap to measure the interdependence of filtering functions. Our framework sheds light on the expressive advantage of multiparameter over monoparameter persistence and suggests potential applications.

Keywords

Cite

@article{arxiv.2506.16985,
  title  = {Topological Correlation},
  author = {Isabella Mastroianni and Ulderico Fugacci},
  journal= {arXiv preprint arXiv:2506.16985},
  year   = {2025}
}
R2 v1 2026-07-01T03:26:36.330Z