The Complexity of Proper Homotopy Equivalence of Graphs

Published 1 Oct 2024 in math.LO, math.GN, and math.GT | (2410.00901v1)

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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