{"paper":{"title":"Local-move-identities for the Z[t,t^{-1}]-Alexander polynomials of 2-links, the alinking number, and high dimensional analogues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eiji Ogasa","submitted_at":"2016-02-25T02:32:48Z","abstract_excerpt":"A well-known identity (Alex+) - (Alex-)=(t^{1/2}-t^{-1/2}) (Alex0) holds for three 1-links L+, L-, and L0 which satisfy a famous local-move-relation.\n  We prove a new local-move-identity for the Z[t,t^{-1}]-Alexander polynomials of 2-links, which is a 2-dimensional analogue of the 1-dimensional one. In the 1-dimensional link case there is a well-known relation between the Alexander-Conway polynomial and the linking number. As its 2-dimensional analogue, we find a relation between the Z[t,t^{-1}]-Alexander polynomials of 2-links and the alinking number of 2-links. We show high dimensional analo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07775","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"}