{"paper":{"title":"Heegaard Floer homology and several families of Brieskorn spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eamonn Tweedy","submitted_at":"2012-06-12T15:00:51Z","abstract_excerpt":"Ozsv\\'ath and Szab\\'o gave a combinatorial description for the Heegaard Floer homology of boundaries of certain negative-definite plumbings. N\\'emethi constructed a remarkable algorithm for executing these computations for almost-rational plumbings, and his work gives a formula computing the invariants for the Brieskorn homology spheres -{\\Sigma} (p,q,pqn + 1). Here we give a formula for HF^{+}(-{\\Sigma}(p,q,pqn-1)), generalizing the one for the n=1 case given by Borodzik and N\\'emethi. We also compute HF^{+} for the families -{\\Sigma}(2,5,k) and -{\\Sigma}(2,7,k)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2558","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"}