{"paper":{"title":"An equivariant Laudenbach-Po\\'enaru theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Evan Scott, Jeffrey Meier","submitted_at":"2025-01-17T19:53:57Z","abstract_excerpt":"A foundational theorem of Laudenbach and Po\\'enaru states that any diffeomorphism of $\\#^n(S^1\\times S^2)$ extends to a diffeomorphism of $\\natural^n(S^1\\times B^3)$. We prove a generalization of this theorem that accounts for the presence of a finite group action on $\\#^n(S^1\\times S^2)$. Our proof is independent of the classical theorem, so by considering the trivial group action, we give a new proof of the classical theorem.\n  Specifically, we show that any finite group action on $\\#^n(S^1\\times S^2)$ extends to a $\\textit{linearly parted}$ action on $\\natural^n(S^1\\times B^3)$ and that any"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.10524","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/2501.10524/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"}