{"paper":{"title":"On the mapping class groups of 4-manifolds with 1-handles","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Boyu Zhang, Jianfeng Lin, Yi Xie","submitted_at":"2025-01-21T01:58:58Z","abstract_excerpt":"We develop a framework that generalizes Budney-Gabai's $W_3$ invariant on $\\pi_0\\textrm{Diff}(S^1\\times D^3,\\partial)$ to 4-manifolds with 1-handles. As applications, we show that if $M=(S^1\\times D^3)\\natural \\hat M$ where $\\hat M$ either has the form $I\\times Y$ or is a punctured aspherical manifold, then the center of the mapping class group of $M$ is of infinite rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11821","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/2501.11821/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"}