{"paper":{"title":"$\\pi_1$-injective bounding and application to 3- and 4-manifolds","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jianfeng Lin, Zhongzi Wang","submitted_at":"2025-06-10T14:35:46Z","abstract_excerpt":"Suppose a closed oriented $n$-manifold $M$ bounds an oriented $(n+1)$-manifold. It is known that $M$ $\\pi_1$-injectively bounds an oriented $(n+1)$-manifold $W$. We prove that $\\pi_1(W)$ can be residually finite if $\\pi_1(M)$ is, and $\\pi_1(W)$ can be finite if $\\pi_1(M)$ is. In particular, each closed 3-manifold $M$ $\\pi_1$-injectively bounds a 4-manifold with residually finite $\\pi_1$, and bounds a 4-manifold with finite $\\pi_1$ if $\\pi_1(M)$ is finite. Applications to 3- and 4-manifolds are given:\n  (1) We study finite group actions on closed 4-manifolds and $\\pi_1$-isomorphic cobordism of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08847","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/2506.08847/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"}