{"paper":{"title":"The Gromov-Hausdorff distance between spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DG"],"primary_cat":"math.MG","authors_text":"Facundo M\\'emoli, Sunhyuk Lim, Zane Smith","submitted_at":"2021-05-03T02:47:29Z","abstract_excerpt":"We provide general upper and lower bounds for the Gromov-Hausdorff distance $d_{\\mathrm{GH}}(\\mathbb{S}^m,\\mathbb{S}^n)$ between spheres $\\mathbb{S}^m$ and $\\mathbb{S}^n$ (endowed with the round metric) for $0\\leq m< n\\leq \\infty$. Some of these lower bounds are based on certain topological ideas related to the Borsuk-Ulam theorem. Via explicit constructions of (optimal) correspondences we prove that our lower bounds are tight in the cases of $d_{\\mathrm{GH}}(\\mathbb{S}^0,\\mathbb{S}^n)$, $d_{\\mathrm{GH}}(\\mathbb{S}^m,\\mathbb{S}^\\infty)$, $d_{\\mathrm{GH}}(\\mathbb{S}^1,\\mathbb{S}^2)$, $d_{\\mathr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.00611","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.00611/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}