{"paper":{"title":"Vanishing theorems and conjectures for the, $\\ell ^2$--homology of right-angled Coxeter groups","license":"","headline":"","cross_cats":["math.AT","math.GT"],"primary_cat":"math.GR","authors_text":"Boris Okun, Michael W Davis","submitted_at":"2001-02-13T20:38:02Z","abstract_excerpt":"Associated to any finite flag complex L there is a right-angled Coxeter group W_L and a cubical complex \\Sigma_L on which W_L acts properly and cocompactly. Its two most salient features are that (1) the link of each vertex of \\Sigma_L is L and (2) \\Sigma_L is contractible. It follows that if L is a triangulation of S^{n-1}, then \\Sigma_L is a contractible n-manifold. We describe a program for proving the Singer Conjecture (on the vanishing of the reduced L^2-homology except in the middle dimension) in the case of \\Sigma_L where L is a triangulation of S^{n-1}. The program succeeds when n < 5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0102104","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"}