{"paper":{"title":"Extendable mapping classes of knotted surfaces obtained by rim surgery in $S^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Weizhe Niu","submitted_at":"2026-05-29T14:51:05Z","abstract_excerpt":"Let $\\Sigma_g^0\\subset S^4$, $g\\ge 3$, be the standard unknotted closed oriented surface, and let $a\\subset\\Sigma_g^0$ be an oriented nonseparating curve. For a nontrivial knot $J\\subset S^3$, let $\\Sigma_{g,a,J}\\subset S^4$ be the surface obtained by ordinary untwisted rim surgery along $a$. Assuming a meridian-longitude rigidity condition on the knot group of $J$, we compute the extendable mapping-class subgroup exactly: \\[ E(\\Sigma_{g,a,J})= \\operatorname{Stab}_{\\operatorname{Mod}(\\Sigma_g)}(q_0)\\cap \\operatorname{Stab}_{\\operatorname{Mod}(\\Sigma_g)}([a]), \\] where $q_0$ is the Rokhlin quad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31383","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/2605.31383/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"}