{"paper":{"title":"On Farber's invariants for simple $2q$-knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jonathan A. Hillman","submitted_at":"2013-02-27T05:24:45Z","abstract_excerpt":"Let $K$ be a simple $2q$-knot with exterior $X$. We show directly how the Farber quintuple $(A,\\Pi,\\alpha,\\ell,\\psi)$ determines the homotopy type of $X$ if the torsion subgroup of $A=\\pi_q(X)$ has odd order. We comment briefly on the possible role of the EHP sequence in recovering the boundary inclusion from the duality pairings $\\ell $ and $\\psi$. Finally we reformulate the Farber quintuple as an hermitian self-duality of an object in an additive category with involution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6665","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"}