{"paper":{"title":"Hyperbolic knots with arbitrarily large torsion order in knot Floer homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Keisuke Himeno, Masakazu Teragaito","submitted_at":"2024-12-30T02:04:58Z","abstract_excerpt":"In knot Floer homology, there are two types of torsion order. One is the minimal power of the action of the variable $U$ to annihilate the $\\mathbb{F}_2[U]$-torsion submodule of the minus version of knot Floer homology $\\mathrm{HFK}^-(K)$. This is introduced by Juh\\'{a}sz, Miller and Zemke, and denoted by $\\mathrm{Ord}(K)$. The other, $\\mathrm{Ord}'(K)$, introduced by Gong and Marengon, is similarly defined for the $\\mathbb{F}_2[U]$-torsion submodule of the unoriented knot Floer homology $\\mathrm{HFK}'(K)$.\n  For both torsion orders, it is known that arbitrarily large values are realized by to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20652","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/2412.20652/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"}