The Complexity of Proper Homotopy Equivalence of Graphs
Logic
2025-11-13 v2 General Topology
Geometric Topology
Abstract
We demonstrate that the proper homotopy equivalence relation for locally finite graphs is Borel complete. Furthermore, among the infinite graphs, there is a comeager equivalence class. As corollaries, we obtain the analogous results for the homeomorphism relation of noncompact surfaces with pants decompositions.
Cite
@article{arxiv.2410.00901,
title = {The Complexity of Proper Homotopy Equivalence of Graphs},
author = {Hannah Hoganson and Jenna Zomback},
journal= {arXiv preprint arXiv:2410.00901},
year = {2025}
}
Comments
Added an appendix proving that the association of the endspace pair to a graph is Borel. 17 pages, 10 figures