The Complexity of Proper Homotopy Equivalence of Graphs

2024/10/01 by Hannah Hoganson, Hoganson, Hannah, Jenna Zomback +1
Mathematics · Decision Sciences · Computer Science · #Advanced Topology and Set Theory #Fuzzy and Soft Set Theory #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.2410.00901

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.

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