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We prove that every isomorphism $\\Mcg(S_1)\\to\\Mcg(S_2)$ is induced by a diffeomorphism $S_1\\to S_2$. This is an analogue of Ivanov's theorem on automorphisms of the mapping class groups of an orientable surface, and also an extension and improvement of the first author's previous result."},"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":"1403.2774","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-11T22:51:39Z","cross_cats_sorted":[],"title_canon_sha256":"70fd62f556336aa3629e78b437b6f7cd238cad63ca2b19c49a1a3525b9fabeb9","abstract_canon_sha256":"40e07c057b7bf26a5efc66d8515b12e0f17466cb5cffb89d5e3d1ed9482da3f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:40.823286Z","signature_b64":"I/aVKSUnI/ivOQmwr5KxH+6MQ9P44IXdw2u93Ofkq54TUFFSInaiFPN/YC5rQffMbHyDYRtSPKMz7Kn8xA3/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"203bcc09c60fc34762806b595ab2e9ccf2c4bc6c2b09104b9a44d1c345d33c48","last_reissued_at":"2026-05-18T00:53:40.822890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:40.822890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphisms of the mapping class group of a nonorientable surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"B{\\l}a\\.zej Szepietowski, Ferihe Atalan","submitted_at":"2014-03-11T22:51:39Z","abstract_excerpt":"Let $S$ be a nonorientable surface of genus $g\\ge 5$ with $n\\ge 0$ punctures, and $\\Mcg(S)$ its mapping class group. We define the complexity of $S$ to be the maximum rank of a free abelian subgroup of $\\Mcg(S)$. Suppose that $S_1$ and $S_2$ are two such surfaces of the same complexity. We prove that every isomorphism $\\Mcg(S_1)\\to\\Mcg(S_2)$ is induced by a diffeomorphism $S_1\\to S_2$. This is an analogue of Ivanov's theorem on automorphisms of the mapping class groups of an orientable surface, and also an extension and improvement of the first author's previous result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2774","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":"1403.2774","created_at":"2026-05-18T00:53:40.822947+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.2774v3","created_at":"2026-05-18T00:53:40.822947+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2774","created_at":"2026-05-18T00:53:40.822947+00:00"},{"alias_kind":"pith_short_12","alias_value":"EA54YCOGB7BU","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"EA54YCOGB7BUOYUA","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"EA54YCOG","created_at":"2026-05-18T12:28:25.294606+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/EA54YCOGB7BUOYUANNMVVMXJZT","json":"https://pith.science/pith/EA54YCOGB7BUOYUANNMVVMXJZT.json","graph_json":"https://pith.science/api/pith-number/EA54YCOGB7BUOYUANNMVVMXJZT/graph.json","events_json":"https://pith.science/api/pith-number/EA54YCOGB7BUOYUANNMVVMXJZT/events.json","paper":"https://pith.science/paper/EA54YCOG"},"agent_actions":{"view_html":"https://pith.science/pith/EA54YCOGB7BUOYUANNMVVMXJZT","download_json":"https://pith.science/pith/EA54YCOGB7BUOYUANNMVVMXJZT.json","view_paper":"https://pith.science/paper/EA54YCOG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.2774&json=true","fetch_graph":"https://pith.science/api/pith-number/EA54YCOGB7BUOYUANNMVVMXJZT/graph.json","fetch_events":"https://pith.science/api/pith-number/EA54YCOGB7BUOYUANNMVVMXJZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EA54YCOGB7BUOYUANNMVVMXJZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EA54YCOGB7BUOYUANNMVVMXJZT/action/storage_attestation","attest_author":"https://pith.science/pith/EA54YCOGB7BUOYUANNMVVMXJZT/action/author_attestation","sign_citation":"https://pith.science/pith/EA54YCOGB7BUOYUANNMVVMXJZT/action/citation_signature","submit_replication":"https://pith.science/pith/EA54YCOGB7BUOYUANNMVVMXJZT/action/replication_record"}},"created_at":"2026-05-18T00:53:40.822947+00:00","updated_at":"2026-05-18T00:53:40.822947+00:00"}