{"paper":{"title":"Harmonic cochains and K-theory for $\\widetilde A_2$ groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.KT"],"primary_cat":"math.OA","authors_text":"Guyan Robertson","submitted_at":"2012-09-25T12:33:04Z","abstract_excerpt":"If $\\Gamma$ is a torsion free $\\widetilde A_2$ group acting on an $\\widetilde A_2$ building $\\Delta$, and $\\fk A_{\\Gamma}$ is the associated boundary $C^*$-algebra, it is proved that $K_0(\\fk A_\\Gamma)\\otimes \\bb R \\cong \\bb R^{2\\beta_2}$, where $\\beta_2=\\dim_\\bb R H^2(\\Gamma, \\bb R)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5590","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"}