{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:4RSWDT5TFNYGRYFXILFLAFQN35","short_pith_number":"pith:4RSWDT5T","schema_version":"1.0","canonical_sha256":"e46561cfb32b7068e0b742cab0160ddf6451760968e86ea795e35f6567f44235","source":{"kind":"arxiv","id":"1206.1196","version":2},"attestation_state":"computed","paper":{"title":"Homomorphisms between diffeomorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Kathryn Mann","submitted_at":"2012-06-06T12:10:19Z","abstract_excerpt":"For r at least 3, p at least 2, we classify all actions of the groups Diff^r_c(R) and Diff^r_+(S1) by C^p -diffeomorphisms on the line and on the circle. This is the same as describing all nontrivial group homomorphisms between groups of compactly supported diffeomorphisms on 1- manifolds. We show that all such actions have an elementary form, which we call topologically diagonal. As an application, we answer a question of Ghys in the 1-manifold case: if M is any closed manifold, and Diff(M)_0 injects into the diffeomorphism group of a 1-manifold, must M be 1 dimensional? We show that the answ"},"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":"1206.1196","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-06-06T12:10:19Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a004d8218c32722f395108135ffe58e904c100dddcc415c0177c1cb45e83591e","abstract_canon_sha256":"b6a33ea2c1026a31834c489e111a1a4ad5c1765bbb79795d453a1824c779a45b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:58.408768Z","signature_b64":"/S7ZVSEMtqvEy/gUl5KmwAbnYMmALppmC37R8PP49Jn+0fiuWWEh9dkXjZnQYm7HWf4gOuabr38PlJdOoxieDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e46561cfb32b7068e0b742cab0160ddf6451760968e86ea795e35f6567f44235","last_reissued_at":"2026-05-18T03:13:58.408044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:58.408044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homomorphisms between diffeomorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Kathryn Mann","submitted_at":"2012-06-06T12:10:19Z","abstract_excerpt":"For r at least 3, p at least 2, we classify all actions of the groups Diff^r_c(R) and Diff^r_+(S1) by C^p -diffeomorphisms on the line and on the circle. This is the same as describing all nontrivial group homomorphisms between groups of compactly supported diffeomorphisms on 1- manifolds. We show that all such actions have an elementary form, which we call topologically diagonal. As an application, we answer a question of Ghys in the 1-manifold case: if M is any closed manifold, and Diff(M)_0 injects into the diffeomorphism group of a 1-manifold, must M be 1 dimensional? We show that the answ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1196","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":"1206.1196","created_at":"2026-05-18T03:13:58.408155+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.1196v2","created_at":"2026-05-18T03:13:58.408155+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1196","created_at":"2026-05-18T03:13:58.408155+00:00"},{"alias_kind":"pith_short_12","alias_value":"4RSWDT5TFNYG","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"4RSWDT5TFNYGRYFX","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"4RSWDT5T","created_at":"2026-05-18T12:26:53.410803+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/4RSWDT5TFNYGRYFXILFLAFQN35","json":"https://pith.science/pith/4RSWDT5TFNYGRYFXILFLAFQN35.json","graph_json":"https://pith.science/api/pith-number/4RSWDT5TFNYGRYFXILFLAFQN35/graph.json","events_json":"https://pith.science/api/pith-number/4RSWDT5TFNYGRYFXILFLAFQN35/events.json","paper":"https://pith.science/paper/4RSWDT5T"},"agent_actions":{"view_html":"https://pith.science/pith/4RSWDT5TFNYGRYFXILFLAFQN35","download_json":"https://pith.science/pith/4RSWDT5TFNYGRYFXILFLAFQN35.json","view_paper":"https://pith.science/paper/4RSWDT5T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.1196&json=true","fetch_graph":"https://pith.science/api/pith-number/4RSWDT5TFNYGRYFXILFLAFQN35/graph.json","fetch_events":"https://pith.science/api/pith-number/4RSWDT5TFNYGRYFXILFLAFQN35/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4RSWDT5TFNYGRYFXILFLAFQN35/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4RSWDT5TFNYGRYFXILFLAFQN35/action/storage_attestation","attest_author":"https://pith.science/pith/4RSWDT5TFNYGRYFXILFLAFQN35/action/author_attestation","sign_citation":"https://pith.science/pith/4RSWDT5TFNYGRYFXILFLAFQN35/action/citation_signature","submit_replication":"https://pith.science/pith/4RSWDT5TFNYGRYFXILFLAFQN35/action/replication_record"}},"created_at":"2026-05-18T03:13:58.408155+00:00","updated_at":"2026-05-18T03:13:58.408155+00:00"}