English

The Rectangle Complex of a Relation

Algebraic Topology 2022-09-29 v2

Abstract

We construct a simplicial complex, the rectangle complex of a relation R, and show that it is homotopy equivalent to the Dowker complex of R. This results in a short and conceptual proof of functorial versions of Dowker's Theorem used in topological data analysis.

Keywords

Cite

@article{arxiv.2207.02018,
  title  = {The Rectangle Complex of a Relation},
  author = {Morten Brun and Lars M. Salbu},
  journal= {arXiv preprint arXiv:2207.02018},
  year   = {2022}
}

Comments

8 pages, 1 figure

R2 v1 2026-06-24T12:14:27.708Z