{"paper":{"title":"On balanced coronas of groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Igor Protasov","submitted_at":"2019-05-17T07:30:22Z","abstract_excerpt":"Let $G$ be an infinite group, $\\kappa$ be an infinite cardinal, $\\kappa\\leq \\mid G\\mid$ and let $\\mathcal{E}_{\\kappa}$ denotes a coarse structure on $G$ with the base $\\{\\{ (x,y): y\\in F x F\\}: F\\in [G]^{<\\kappa}\\}$. We prove that if either $\\kappa< \\mid G\\mid$ or $\\kappa= \\mid G\\mid$ and $\\kappa$ is singular then the Higson's corona $\\nu _{\\kappa} (G)$ of the coarse space $(G, \\mathcal{E}_{\\kappa})$ is a singleton. If $\\kappa= \\mid G\\mid$ and $\\kappa$ is regular then $\\nu _{\\kappa} (G)$ contains a copy of the space $U_{\\kappa}$ of $\\kappa$-uniform ultrafilters on $\\kappa$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07142","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}