{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:BXXT5AVNA24DXTXOYOSBQZDE4P","short_pith_number":"pith:BXXT5AVN","schema_version":"1.0","canonical_sha256":"0def3e82ad06b83bceeec3a4186464e3c09af52e464ff174cf5574bca82490ae","source":{"kind":"arxiv","id":"0901.2314","version":3},"attestation_state":"computed","paper":{"title":"Representations of surface groups in the projective general linear group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Andr\\'e Oliveira","submitted_at":"2009-01-15T17:02:05Z","abstract_excerpt":"Given a closed, oriented surface X of genus g>1, and a semisimple Lie group G, let R_G be the moduli space of reductive representations of the fundamental group of X in G. We determine the number of connected components of R_PGL(n,R), for n>=4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in R_SL(3,R) is homotopically equivalent to R_SO(3)"},"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":"0901.2314","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-01-15T17:02:05Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"8fa389cecbd1771dffa90dd81e0f614673bfa5afad57423bd0ddbcdd54d30037","abstract_canon_sha256":"71fc8fc917fc12100d1dac94594bcfc33a53058fe1bb6ec180f410cf9f049273"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:48.145593Z","signature_b64":"gAXDQXMzcYHbL81ojpReH/uRImX0HAyJRP6XseD5AbN/uScnMjF7Fhd2x4fsx5pXUQagEt9nFM+qwOE9TjFzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0def3e82ad06b83bceeec3a4186464e3c09af52e464ff174cf5574bca82490ae","last_reissued_at":"2026-05-17T23:48:48.144975Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:48.144975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representations of surface groups in the projective general linear group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Andr\\'e Oliveira","submitted_at":"2009-01-15T17:02:05Z","abstract_excerpt":"Given a closed, oriented surface X of genus g>1, and a semisimple Lie group G, let R_G be the moduli space of reductive representations of the fundamental group of X in G. We determine the number of connected components of R_PGL(n,R), for n>=4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in R_SL(3,R) is homotopically equivalent to R_SO(3)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2314","kind":"arxiv","version":3},"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":"0901.2314","created_at":"2026-05-17T23:48:48.145069+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.2314v3","created_at":"2026-05-17T23:48:48.145069+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.2314","created_at":"2026-05-17T23:48:48.145069+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXXT5AVNA24D","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXXT5AVNA24DXTXO","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXXT5AVN","created_at":"2026-05-18T12:25:58.837520+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/BXXT5AVNA24DXTXOYOSBQZDE4P","json":"https://pith.science/pith/BXXT5AVNA24DXTXOYOSBQZDE4P.json","graph_json":"https://pith.science/api/pith-number/BXXT5AVNA24DXTXOYOSBQZDE4P/graph.json","events_json":"https://pith.science/api/pith-number/BXXT5AVNA24DXTXOYOSBQZDE4P/events.json","paper":"https://pith.science/paper/BXXT5AVN"},"agent_actions":{"view_html":"https://pith.science/pith/BXXT5AVNA24DXTXOYOSBQZDE4P","download_json":"https://pith.science/pith/BXXT5AVNA24DXTXOYOSBQZDE4P.json","view_paper":"https://pith.science/paper/BXXT5AVN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.2314&json=true","fetch_graph":"https://pith.science/api/pith-number/BXXT5AVNA24DXTXOYOSBQZDE4P/graph.json","fetch_events":"https://pith.science/api/pith-number/BXXT5AVNA24DXTXOYOSBQZDE4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXXT5AVNA24DXTXOYOSBQZDE4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXXT5AVNA24DXTXOYOSBQZDE4P/action/storage_attestation","attest_author":"https://pith.science/pith/BXXT5AVNA24DXTXOYOSBQZDE4P/action/author_attestation","sign_citation":"https://pith.science/pith/BXXT5AVNA24DXTXOYOSBQZDE4P/action/citation_signature","submit_replication":"https://pith.science/pith/BXXT5AVNA24DXTXOYOSBQZDE4P/action/replication_record"}},"created_at":"2026-05-17T23:48:48.145069+00:00","updated_at":"2026-05-17T23:48:48.145069+00:00"}