{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L4NB4I3QUIEH42JRHFEI3DRPPT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5b328a0e23c99cf9fd7b6859268b7faeef28b2cd7274d5a17a892cde17f901c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-12-20T13:48:27Z","title_canon_sha256":"f7940866294937552589088ba6c9190862b0f09ecc14d0f3b3eae02c8ca88ed1"},"schema_version":"1.0","source":{"id":"1901.01125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.01125","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"arxiv_version","alias_value":"1901.01125v1","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01125","created_at":"2026-05-17T23:56:57Z"},{"alias_kind":"pith_short_12","alias_value":"L4NB4I3QUIEH","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L4NB4I3QUIEH42JR","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L4NB4I3Q","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:e64ed4f4b98daca6b517e98d8d12a31269cfe1dc61e8f3ccd19f603f3ecdbfe6","target":"graph","created_at":"2026-05-17T23:56:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $H_n$ be the $n$-th group homology functor (with integer coeffcients) and let $\\{G_i\\} _ {i \\in \\mathbb{N}}$ be any tower of groups such that all maps $G_{i+1} \\to G_i$ are surjective. In this work we study kernel and cokernel of the following natural map: $$H_n(\\varprojlim G_i) \\to \\varprojlim H_n(G_i)$$ For $n=1$ Barnea and Shelah [BS] proved that this map is surjective and its kernel is a cotorsion group for any such tower $\\{G_i\\} _ {i \\in \\mathbb{N}}$. We show that for $n=2$ the kernel can be non-cotorsion group even in the case when all $G_i$ are abelian and after it we study these k","authors_text":"Danil Akhtiamov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-12-20T13:48:27Z","title":"Homologies of inverse limits of groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01125","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6ff229a8d3873094d6fd6a262936bcf5eb58e861b13f4739d69a4ae0fa1c56e4","target":"record","created_at":"2026-05-17T23:56:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5b328a0e23c99cf9fd7b6859268b7faeef28b2cd7274d5a17a892cde17f901c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-12-20T13:48:27Z","title_canon_sha256":"f7940866294937552589088ba6c9190862b0f09ecc14d0f3b3eae02c8ca88ed1"},"schema_version":"1.0","source":{"id":"1901.01125","kind":"arxiv","version":1}},"canonical_sha256":"5f1a1e2370a2087e693139488d8e2f7cd61b4bb705616b8c032f3c3e196506fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f1a1e2370a2087e693139488d8e2f7cd61b4bb705616b8c032f3c3e196506fa","first_computed_at":"2026-05-17T23:56:57.011932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:57.011932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N7mVxHrKSNCPgNcJ7Xl3oYEtcNOCVYAKcc1e36Zo3UkSddofnsC4b72wzGUs/Vfwgy0vh4dmDLk7OpNdno+RAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:57.012423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.01125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ff229a8d3873094d6fd6a262936bcf5eb58e861b13f4739d69a4ae0fa1c56e4","sha256:e64ed4f4b98daca6b517e98d8d12a31269cfe1dc61e8f3ccd19f603f3ecdbfe6"],"state_sha256":"eac56a31b910af4805e665dd3ccfa3bda60b18d03419de0d7329c4d72af000c7"}