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Let $\\rho:\\pi_1(X)\\to GL(n,\\mathbb{C})$ be a representation, denote by $H^*(X,\\rho)$ the corresponding twisted cohomology of $X$. Denote by $\\rho_0$ the restriction of $\\rho$ to $\\pi_1(M)$, and by $\\rho^*_0$ the antirepresentation conjugate to $\\rho_0$. We construct from these data an automorphism of the group $H_*(M,\\rho^*_0)$, that we call the twisted monodromy homomor"},"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":"1701.06677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-23T23:35:08Z","cross_cats_sorted":["math.AT","math.DG"],"title_canon_sha256":"1409426e2a6f919e5d4f1657c56954ad4a4e021efd359a0434ab15bd80bf9210","abstract_canon_sha256":"c7ff1e91a694a0352b53db9c9b6448131803599880881a416f529f0f310072c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:12.388593Z","signature_b64":"jfDGp7c/JUl7ailvKKj9l1bRrUQiCJGFX1TbfoqifvbD0knPwl1eVwW3K4a1wAI4dVxFWpxiXdohHhSHUXiBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96e38bc00d0e6b36d11868e82731c95cc2feb4f6b98ad293c7d04bec531763ba","last_reissued_at":"2026-05-18T00:52:12.388087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:12.388087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twisted monodromy homomorphisms and Massey products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DG"],"primary_cat":"math.AG","authors_text":"Andrei Pajitnov","submitted_at":"2017-01-23T23:35:08Z","abstract_excerpt":"Let $\\phi: M\\to M$ be a diffeomorphism of a $C^\\infty$ compact connected manifold, and $X$ its mapping torus. There is a natural fibration $p:X\\to S^1$, denote by $\\xi\\in H^1(X, \\mathbb{Z})$ the corresponding cohomology class. Let $\\rho:\\pi_1(X)\\to GL(n,\\mathbb{C})$ be a representation, denote by $H^*(X,\\rho)$ the corresponding twisted cohomology of $X$. Denote by $\\rho_0$ the restriction of $\\rho$ to $\\pi_1(M)$, and by $\\rho^*_0$ the antirepresentation conjugate to $\\rho_0$. We construct from these data an automorphism of the group $H_*(M,\\rho^*_0)$, that we call the twisted monodromy homomor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06677","kind":"arxiv","version":1},"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":"1701.06677","created_at":"2026-05-18T00:52:12.388161+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.06677v1","created_at":"2026-05-18T00:52:12.388161+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06677","created_at":"2026-05-18T00:52:12.388161+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3RYXQANBZVT","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3RYXQANBZVTNUIY","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3RYXQAN","created_at":"2026-05-18T12:31:43.269735+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/S3RYXQANBZVTNUIYNDUCOMOJLT","json":"https://pith.science/pith/S3RYXQANBZVTNUIYNDUCOMOJLT.json","graph_json":"https://pith.science/api/pith-number/S3RYXQANBZVTNUIYNDUCOMOJLT/graph.json","events_json":"https://pith.science/api/pith-number/S3RYXQANBZVTNUIYNDUCOMOJLT/events.json","paper":"https://pith.science/paper/S3RYXQAN"},"agent_actions":{"view_html":"https://pith.science/pith/S3RYXQANBZVTNUIYNDUCOMOJLT","download_json":"https://pith.science/pith/S3RYXQANBZVTNUIYNDUCOMOJLT.json","view_paper":"https://pith.science/paper/S3RYXQAN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.06677&json=true","fetch_graph":"https://pith.science/api/pith-number/S3RYXQANBZVTNUIYNDUCOMOJLT/graph.json","fetch_events":"https://pith.science/api/pith-number/S3RYXQANBZVTNUIYNDUCOMOJLT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3RYXQANBZVTNUIYNDUCOMOJLT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3RYXQANBZVTNUIYNDUCOMOJLT/action/storage_attestation","attest_author":"https://pith.science/pith/S3RYXQANBZVTNUIYNDUCOMOJLT/action/author_attestation","sign_citation":"https://pith.science/pith/S3RYXQANBZVTNUIYNDUCOMOJLT/action/citation_signature","submit_replication":"https://pith.science/pith/S3RYXQANBZVTNUIYNDUCOMOJLT/action/replication_record"}},"created_at":"2026-05-18T00:52:12.388161+00:00","updated_at":"2026-05-18T00:52:12.388161+00:00"}