{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MJINZBF5V2EWUM2PX4GF75NWB6","short_pith_number":"pith:MJINZBF5","schema_version":"1.0","canonical_sha256":"6250dc84bdae896a334fbf0c5ff5b60fbe3c5e8e98b3cef2b18989c8face9131","source":{"kind":"arxiv","id":"1409.3142","version":2},"attestation_state":"computed","paper":{"title":"A cohomological framework for homotopy moment maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.SG"],"primary_cat":"math.DG","authors_text":"Camille Laurent-Gengoux, Marco Zambon, Yael Fregier","submitted_at":"2014-09-10T16:17:45Z","abstract_excerpt":"Given a Lie group acting on a manifold $M$ preserving a closed $n+1$-form $\\omega$, the notion of homotopy moment map for this action was introduced in Callies-Fregier-Rogers-Zambon [6], in terms of $L_{\\infty}$-algebra morphisms. In this note we describe homotopy moment maps as coboundaries of a certain complex. This description simplifies greatly computations, and we use it to study various properties of homotopy moment maps: their relation to equivariant cohomology, their obstruction theory, how they induce new ones on mapping spaces, and their equivalences. The results we obtain extend som"},"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":"1409.3142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-10T16:17:45Z","cross_cats_sorted":["math.QA","math.SG"],"title_canon_sha256":"4f0eedd2996c191a4be3b1a3855e96e1b0a164a8a07ea0b360e4a824d4ca2b68","abstract_canon_sha256":"0cec41f871aa509ebae0b6bc86184610d3fdb5252f5a6b34a72738873e3eec8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:43.937313Z","signature_b64":"oWSajO1i5IJlj6utcv4MkAWN1ENlmn6vYCZPwTTVMB3zus/t8djq2AlnyGfTIq78QvhulNNuSrt80LcsU569DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6250dc84bdae896a334fbf0c5ff5b60fbe3c5e8e98b3cef2b18989c8face9131","last_reissued_at":"2026-05-18T01:11:43.936982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:43.936982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A cohomological framework for homotopy moment maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.SG"],"primary_cat":"math.DG","authors_text":"Camille Laurent-Gengoux, Marco Zambon, Yael Fregier","submitted_at":"2014-09-10T16:17:45Z","abstract_excerpt":"Given a Lie group acting on a manifold $M$ preserving a closed $n+1$-form $\\omega$, the notion of homotopy moment map for this action was introduced in Callies-Fregier-Rogers-Zambon [6], in terms of $L_{\\infty}$-algebra morphisms. In this note we describe homotopy moment maps as coboundaries of a certain complex. This description simplifies greatly computations, and we use it to study various properties of homotopy moment maps: their relation to equivariant cohomology, their obstruction theory, how they induce new ones on mapping spaces, and their equivalences. The results we obtain extend som"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3142","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":"1409.3142","created_at":"2026-05-18T01:11:43.937036+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.3142v2","created_at":"2026-05-18T01:11:43.937036+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3142","created_at":"2026-05-18T01:11:43.937036+00:00"},{"alias_kind":"pith_short_12","alias_value":"MJINZBF5V2EW","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"MJINZBF5V2EWUM2P","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"MJINZBF5","created_at":"2026-05-18T12:28:38.356838+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/MJINZBF5V2EWUM2PX4GF75NWB6","json":"https://pith.science/pith/MJINZBF5V2EWUM2PX4GF75NWB6.json","graph_json":"https://pith.science/api/pith-number/MJINZBF5V2EWUM2PX4GF75NWB6/graph.json","events_json":"https://pith.science/api/pith-number/MJINZBF5V2EWUM2PX4GF75NWB6/events.json","paper":"https://pith.science/paper/MJINZBF5"},"agent_actions":{"view_html":"https://pith.science/pith/MJINZBF5V2EWUM2PX4GF75NWB6","download_json":"https://pith.science/pith/MJINZBF5V2EWUM2PX4GF75NWB6.json","view_paper":"https://pith.science/paper/MJINZBF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.3142&json=true","fetch_graph":"https://pith.science/api/pith-number/MJINZBF5V2EWUM2PX4GF75NWB6/graph.json","fetch_events":"https://pith.science/api/pith-number/MJINZBF5V2EWUM2PX4GF75NWB6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MJINZBF5V2EWUM2PX4GF75NWB6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MJINZBF5V2EWUM2PX4GF75NWB6/action/storage_attestation","attest_author":"https://pith.science/pith/MJINZBF5V2EWUM2PX4GF75NWB6/action/author_attestation","sign_citation":"https://pith.science/pith/MJINZBF5V2EWUM2PX4GF75NWB6/action/citation_signature","submit_replication":"https://pith.science/pith/MJINZBF5V2EWUM2PX4GF75NWB6/action/replication_record"}},"created_at":"2026-05-18T01:11:43.937036+00:00","updated_at":"2026-05-18T01:11:43.937036+00:00"}