{"paper":{"title":"Genus, Fiberedness, $\\tau$ and $\\epsilon$ of Satellite Knots with $n$-Twisted Generalized Mazur patterns","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Holt Bodish","submitted_at":"2024-05-14T16:55:15Z","abstract_excerpt":"We study a family of $(1,1)$-pattern knots that generalize the Mazur pattern, and compute the concordance invariants $\\tau$ and $\\epsilon$ of $n$-twisted satellites formed from these patterns. We show that none of the $n$-twisted patterns from this family act surjectively on the smooth or rational concordance group. We also determine when the $n$-twisted generalized Mazur patterns are fibered in the solid torus, compute their genus in $S^1 \\times D^2$, and show that $n$-twisted satellites with generalized Mazur patterns and non-trivial companions are not Floer thin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.08763","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/2405.08763/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"}