Locally Euclidean Discretized Graph Configuration Spaces
Geometric Topology
2026-07-09 v1
Abstract
We investigate discretized graph configuration spaces as defined by Aaron Abrams in his PhD thesis in 2000. Specifically, we extend Abrams' work by completely classifying which ones admitted by simple graphs are homeomorphic to closed manifolds. In the process of doing so, we develop techniques to translate topological properties of these spaces into graph theoretic ones.
Cite
@article{arxiv.2607.08810,
title = {Locally Euclidean Discretized Graph Configuration Spaces},
author = {Justin Murray and Zach Wilcher},
journal= {arXiv preprint arXiv:2607.08810},
year = {2026}
}
Comments
29 pages, 35 figures. This work is based on the second author's Master's Thesis at Ball State University