{"paper":{"title":"The Dehn twist on a connected sum of two homology tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Haochen Qiu","submitted_at":"2024-10-03T13:11:41Z","abstract_excerpt":"Kronheimer-Mrowka shows that the Dehn twist along a $3$-sphere in the neck of two $K3$ surfaces is not smoothly isotopic to the identity. Their result requires that the manifolds are simply connected and the signature of one of them is $16 \\mod 32$. We generalize the Pin$(2)$-equivariant family Bauer-Furuta invariant to nonsimply connected manifolds, and construct a refinement of this invariant. We use it to show that, if $X_1,X_2$ are two homology tori such that the determinants $r_1,r_2$ of them are odd, then the Dehn twist along a $3$-sphere in the neck of $X_1\\# X_2$ is not smoothly isotop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.02461","kind":"arxiv","version":2},"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/2410.02461/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"}