{"paper":{"title":"Linking numbers in rational homology 3-spheres, cyclic branched covers and infinite cyclic covers","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akira Yasuhara, Jozef H. Przytycki","submitted_at":"2001-11-19T07:02:40Z","abstract_excerpt":"We study the linking numbers in a rational homology 3-sphere and in the infinite cyclic cover of the complement of a knot. They take values in $\\Bbb Q$ and in ${Q}({\\Bbb Z}[t,t^{-1}])$ respectively, where ${Q}({\\Bbb Z}[t,t^{-1}])$ denotes the quotient field of ${\\Bbb Z}[t,t^{-1}]$. It is known that the modulo-$\\Bbb Z$ linking number in the rational homology 3-sphere is determined by the linking matrix of the framed link and that the modulo-${\\Bbb Z}[t,t^{-1}]$ linking number in the infinite cyclic cover of the complement of a knot is determined by the Seifert matrix of the knot. We eliminate `"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0111203","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0111203/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}