{"paper":{"title":"Borel structurability by locally finite simplicial complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Ruiyuan Chen","submitted_at":"2017-02-23T01:12:17Z","abstract_excerpt":"We show that every countable Borel equivalence relation structurable by $n$-dimensional contractible simplicial complexes embeds into one which is structurable by such complexes with the further property that each vertex belongs to at most $M_n := 2^{n-1}(n^2+3n+2)-2$ edges; this generalizes a result of Jackson-Kechris-Louveau in the case $n = 1$. The proof is based on that of a classical result of Whitehead on countable CW-complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07057","kind":"arxiv","version":2},"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"}