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Based upon this, we investigate what kinds of closed manifolds admit locally standard $(\\Z_2)^n$-actions; especially for the 3-dimensional case.\n  Suppose $M$ is an orientable closed connected 3-manifold. When $H_1(M;\\Z_2)=0$, it is shown that $M$ admits a loc"},"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":"0807.3062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-07-21T08:04:43Z","cross_cats_sorted":["math.AT","math.CO"],"title_canon_sha256":"647d5b62200f016dde3f2ee46970d9e4b36208324d22f66aa3d4f6e424decd52","abstract_canon_sha256":"9f10365a16ccc46e5eaea08aa5cfb3ccac85e894d5202b822d75a9d68854cf4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:48.237270Z","signature_b64":"ustEqSkfZKdX8sJzwPu65NhmmElSDBQ42nsElReK0BIyop7iAn/41zlT6cqqvjyxSa9P5NLZNxeZP6xXTvYBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"658326c219b805255642e24b598826dafc27413e359fc38bddabb09f779d43bd","last_reissued_at":"2026-05-18T01:18:48.236587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:48.236587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On 3-manifolds with locally-standard (Z_2)^3-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.GT","authors_text":"Li Yu, Zhi L\\\"u","submitted_at":"2008-07-21T08:04:43Z","abstract_excerpt":"As a generalization of Davis-Januszkiewicz theory, there is an essential link between locally standard $(\\Z_2)^n$-actions (or $T^n$-actions) actions and nice manifolds with corners, so that a class of nicely behaved equivariant cut-and-paste operations on locally standard actions can be carried out in step on nice manifolds with corners. Based upon this, we investigate what kinds of closed manifolds admit locally standard $(\\Z_2)^n$-actions; especially for the 3-dimensional case.\n  Suppose $M$ is an orientable closed connected 3-manifold. When $H_1(M;\\Z_2)=0$, it is shown that $M$ admits a loc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3062","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0807.3062","created_at":"2026-05-18T01:18:48.236717+00:00"},{"alias_kind":"arxiv_version","alias_value":"0807.3062v2","created_at":"2026-05-18T01:18:48.236717+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.3062","created_at":"2026-05-18T01:18:48.236717+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWBSNQQZXACS","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWBSNQQZXACSKVSC","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWBSNQQZ","created_at":"2026-05-18T12:25:57.157939+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MWBSNQQZXACSKVSC4JFVTCBG3L","json":"https://pith.science/pith/MWBSNQQZXACSKVSC4JFVTCBG3L.json","graph_json":"https://pith.science/api/pith-number/MWBSNQQZXACSKVSC4JFVTCBG3L/graph.json","events_json":"https://pith.science/api/pith-number/MWBSNQQZXACSKVSC4JFVTCBG3L/events.json","paper":"https://pith.science/paper/MWBSNQQZ"},"agent_actions":{"view_html":"https://pith.science/pith/MWBSNQQZXACSKVSC4JFVTCBG3L","download_json":"https://pith.science/pith/MWBSNQQZXACSKVSC4JFVTCBG3L.json","view_paper":"https://pith.science/paper/MWBSNQQZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0807.3062&json=true","fetch_graph":"https://pith.science/api/pith-number/MWBSNQQZXACSKVSC4JFVTCBG3L/graph.json","fetch_events":"https://pith.science/api/pith-number/MWBSNQQZXACSKVSC4JFVTCBG3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWBSNQQZXACSKVSC4JFVTCBG3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWBSNQQZXACSKVSC4JFVTCBG3L/action/storage_attestation","attest_author":"https://pith.science/pith/MWBSNQQZXACSKVSC4JFVTCBG3L/action/author_attestation","sign_citation":"https://pith.science/pith/MWBSNQQZXACSKVSC4JFVTCBG3L/action/citation_signature","submit_replication":"https://pith.science/pith/MWBSNQQZXACSKVSC4JFVTCBG3L/action/replication_record"}},"created_at":"2026-05-18T01:18:48.236717+00:00","updated_at":"2026-05-18T01:18:48.236717+00:00"}