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Let $f \\colon \\widetilde{I}_{2n,k} \\rightarrow \\widetilde{I}_{2m,l} $ be a map between two oriented isotropic Grassmannians of the same dimension, where $k,l \\geq 2$. We show that either $(n,k) = (m,l)$ or the degree of $f$ must be zero. Let $\\mathbb{R}\\widetilde{G}_{m,l}$ denote the oriented real Grassmann manifold. For $k,l \\geq 2$ and $\\dim{\\widetilde{I}_{2n,k}} = \\dim{\\mathbb{R}\\widetilde{G}_{m,l}}$, we also show that the degree of m"},"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":"1508.02143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-10T07:03:21Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"621eff14295a87dfc2246b787e4f6bb867d99a1e520eec66ba2aa7e91fee4cea","abstract_canon_sha256":"98a1ca914f3b0f95a001d83c64695af34098eae4df2438a4fa7d17a29af7b29b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:34.067698Z","signature_b64":"j+TTi5//tmuWcciak8f8yphEWfD5vlz9B8vvr23eE5J5Kgvy8/sTjvk7tjW+ovgDULwySYhbeuLPLF7G9cJHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7b86052ced815a2fa05bd08b42c8690191aa2b5d54ca33ab2272b2535c898c6","last_reissued_at":"2026-05-18T01:35:34.067011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:34.067011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degrees of Maps between Isotropic Grassmann Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Samik Basu, Swagata Sarkar","submitted_at":"2015-08-10T07:03:21Z","abstract_excerpt":"Let $\\widetilde{I}_{2n,k}$ denote the space of $k$-dimensional, oriented isotropic subspaces of $\\mathbb{R}^{2n}$, called the oriented isotropic Grassmannian. 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For $k,l \\geq 2$ and $\\dim{\\widetilde{I}_{2n,k}} = \\dim{\\mathbb{R}\\widetilde{G}_{m,l}}$, we also show that the degree of m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02143","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":"1508.02143","created_at":"2026-05-18T01:35:34.067138+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.02143v1","created_at":"2026-05-18T01:35:34.067138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02143","created_at":"2026-05-18T01:35:34.067138+00:00"},{"alias_kind":"pith_short_12","alias_value":"664GAUWO3AK2","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"664GAUWO3AK2F6QF","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"664GAUWO","created_at":"2026-05-18T12:29:07.941421+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/664GAUWO3AK2F6QFXUELILEGSA","json":"https://pith.science/pith/664GAUWO3AK2F6QFXUELILEGSA.json","graph_json":"https://pith.science/api/pith-number/664GAUWO3AK2F6QFXUELILEGSA/graph.json","events_json":"https://pith.science/api/pith-number/664GAUWO3AK2F6QFXUELILEGSA/events.json","paper":"https://pith.science/paper/664GAUWO"},"agent_actions":{"view_html":"https://pith.science/pith/664GAUWO3AK2F6QFXUELILEGSA","download_json":"https://pith.science/pith/664GAUWO3AK2F6QFXUELILEGSA.json","view_paper":"https://pith.science/paper/664GAUWO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.02143&json=true","fetch_graph":"https://pith.science/api/pith-number/664GAUWO3AK2F6QFXUELILEGSA/graph.json","fetch_events":"https://pith.science/api/pith-number/664GAUWO3AK2F6QFXUELILEGSA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/664GAUWO3AK2F6QFXUELILEGSA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/664GAUWO3AK2F6QFXUELILEGSA/action/storage_attestation","attest_author":"https://pith.science/pith/664GAUWO3AK2F6QFXUELILEGSA/action/author_attestation","sign_citation":"https://pith.science/pith/664GAUWO3AK2F6QFXUELILEGSA/action/citation_signature","submit_replication":"https://pith.science/pith/664GAUWO3AK2F6QFXUELILEGSA/action/replication_record"}},"created_at":"2026-05-18T01:35:34.067138+00:00","updated_at":"2026-05-18T01:35:34.067138+00:00"}