{"paper":{"title":"Expanders and box spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.GR","authors_text":"Alain Valette, Ana Khukhro","submitted_at":"2015-09-04T10:14:52Z","abstract_excerpt":"We consider box spaces of finitely generated, residually finite groups $G$, and try to distinguish them up to coarse equivalence. We show that, for $n\\geq 2$, the group $SL_n(\\mathbb{Z})$ has a continuum of box spaces which are pairwise non-coarsely equivalent expanders. Moreover, varying the integer $n\\geq 3$, expanders given as box spaces of $SL_n(\\mathbb{Z})$ are pairwise inequivalent; similarly, varying the prime $p$, expanders given as box spaces of $SL_2(\\mathbb{Z}[\\sqrt{p}])$ are pairwise inequivalent.\n  A strong form of non-expansion for a box space is the existence of $\\alpha\\in]0,1]$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01394","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"}