{"paper":{"title":"Boundary Dehn twists are often commutators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Boundary Dehn twists on punctured 4-manifolds are commutators of two diffeomorphisms","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ayodeji Lindblad","submitted_at":"2026-04-14T18:17:03Z","abstract_excerpt":"For $X$ any complete intersection of even complex dimension or any connected sum thereof (or, more generally, any space among certain broad classes of smooth manifolds), we concretely construct diffeomorphisms $a,c$ of punctured $X$ rel boundary whose commutator $[a,c]$ represents the smooth mapping class (rel boundary) of the boundary Dehn twist. This shows that boundary Dehn twists on 4-manifolds known to be nontrivial in the smooth mapping class group rel boundary by work of Baraglia-Konno, Kronheimer-Mrowka, J. Lin, and Tilton become trivial after abelianization, generalizing work of Y. Li"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For X any complete intersection of even complex dimension or any connected sum thereof (or, more generally, any space among certain broad classes of smooth manifolds), we concretely construct orientation-preserving diffeomorphisms a,c of punctured X rel boundary whose commutator [a,c] represents the smooth mapping class rel boundary of the boundary Dehn twist.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The explicit constructions of diffeomorphisms a and c exist and satisfy the commutator relation for the stated broad classes of smooth 4-manifolds, and that the boundary Dehn twist is indeed the image of this commutator in the mapping class group rel boundary.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Boundary Dehn twists on punctured even-dimensional complete intersections and connected sums are commutators in the smooth mapping class group rel boundary, hence trivial after abelianization.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Boundary Dehn twists on punctured 4-manifolds are commutators of two diffeomorphisms","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ea59da224e55509203d5b82a19a486853e32c0c0c1b29c9951f018b63337c11b"},"source":{"id":"2604.13194","kind":"arxiv","version":2},"verdict":{"id":"b4565639-f3f9-4172-a2bd-91e28f11e7be","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T13:44:03.384380Z","strongest_claim":"For X any complete intersection of even complex dimension or any connected sum thereof (or, more generally, any space among certain broad classes of smooth manifolds), we concretely construct orientation-preserving diffeomorphisms a,c of punctured X rel boundary whose commutator [a,c] represents the smooth mapping class rel boundary of the boundary Dehn twist.","one_line_summary":"Boundary Dehn twists on punctured even-dimensional complete intersections and connected sums are commutators in the smooth mapping class group rel boundary, hence trivial after abelianization.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The explicit constructions of diffeomorphisms a and c exist and satisfy the commutator relation for the stated broad classes of smooth 4-manifolds, and that the boundary Dehn twist is indeed the image of this commutator in the mapping class group rel boundary.","pith_extraction_headline":"Boundary Dehn twists on punctured 4-manifolds are commutators of two diffeomorphisms"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.13194/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"}