English

Bipath Persistence

Algebraic Topology 2024-04-04 v1 Representation Theory

Abstract

In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology, which can be used to study the persistence of topological features across a pair of filtrations connected at their ends, to compare the two filtrations. In this setting, interval-decomposability is guaranteed, and we provide an algorithm for computing persistence diagrams for bipath persistent homology and discuss the interpretation of bipath persistence diagrams.

Keywords

Cite

@article{arxiv.2404.02536,
  title  = {Bipath Persistence},
  author = {Toshitaka Aoki and Emerson G. Escolar and Shunsuke Tada},
  journal= {arXiv preprint arXiv:2404.02536},
  year   = {2024}
}

Comments

22 pages

R2 v1 2026-06-28T15:42:43.865Z