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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.08847","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GT","submitted_at":"2025-06-10T14:35:46Z","cross_cats_sorted":[],"title_canon_sha256":"dc0abd9370714eb82f0772edf89944315984ea5a476088f90d3aeff05e9ee3bb","abstract_canon_sha256":"bdc2c22c47cff2f576c62a54d28e617a93f2180f1ed7f44241224e6a07cec585"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:53.994658Z","signature_b64":"UoVRchye1R2TTbxNVPzHlhbs7OcvEiXSSPotFt8gpJ8UMD/+jtgc6P40lllFGCsrzzKzYDvTH8TsEs6EdlgFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc0061ad7b9c8d0b20c7193ffdf29817b0d238ba5d06f2d1cad4758734b50fbb","last_reissued_at":"2026-07-05T11:19:53.994179Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:53.994179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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