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arXiv · 2410.00901

The Complexity of Proper Homotopy Equivalence of Graphs

Hannah Hoganson·Jenna Zomback
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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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Hannah Hoganson, Jenna Zomback. 2024-10-01. The Complexity of Proper Homotopy Equivalence of Graphs. https://arxiv.org/abs/2410.00901

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