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arXiv:2410.00901 [math.LO]AbstractReferencesReviewsResources

The Complexity of Proper Homotopy Equivalence of Graphs

Hannah Hoganson, Jenna Zomback

Published 2024-10-01Version 1

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.

Comments: 13 pages, 12 figures
Categories: math.LO, math.GN, math.GT
Subjects: 03E15, 54H05, 57M99
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