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Dehn-Nielsen-Baer theorem 1graph theory 1infinite-type surfaces 1mapping class groups 1proper homotopy equivalence 1

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math.LO2025

The Complexity of Proper Homotopy Equivalence of Graphs

Hannah Hoganson, Jenna Zomback

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 cl…