The Complexity of Proper Homotopy Equivalence of Graphs
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911259959492608 |
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| author | Hoganson, Hannah Zomback, Jenna |
| author_facet | Hoganson, Hannah Zomback, Jenna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00901 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Complexity of Proper Homotopy Equivalence of Graphs Hoganson, Hannah Zomback, Jenna Logic General Topology Geometric Topology 03E15, 54H05, 57M99 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. |
| title | The Complexity of Proper Homotopy Equivalence of Graphs |
| topic | Logic General Topology Geometric Topology 03E15, 54H05, 57M99 |
| url | https://arxiv.org/abs/2410.00901 |