Graphs and Their Vietoris-Rips Complexes Have the Same Pseudotopological Weak Homotopy Type
Algebraic Topology
2024-07-02 v2 General Topology
Abstract
In this document, we propose a bridge between the graphs and the geometric realizations of their Vietoris Rips complexes, i.e. Graphs, with their canonical \v{C}ech closure structure, have the same homotopy type that the realization of their Vietoris Rips complex.
Cite
@article{arxiv.2406.00149,
title = {Graphs and Their Vietoris-Rips Complexes Have the Same Pseudotopological Weak Homotopy Type},
author = {Jonathan Treviño-Marroquín},
journal= {arXiv preprint arXiv:2406.00149},
year = {2024}
}
Comments
19 pages, 4 figures. The notation of the convex transformation was changed to emphases in the importance of the triangulations