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As an application, we show the existence of a point $A\\in G_{l}(\\bc^m)$ such that the vector space $f(A)$ is contained in $A$; here $\\mathbb{C}^n$ is regarded as a vector subspace of $\\mathbb{C}^m\\cong \\bc^n\\oplus\\bc^{m-n}.$"},"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":"1312.4743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-17T12:21:22Z","cross_cats_sorted":[],"title_canon_sha256":"190916df3abcb7ef11bf70d7780d0ef2bf4c540f2fed218e2153edf45d597b8e","abstract_canon_sha256":"635dfb36b9e271c2d24d8bb1989a6262e40544aad342fe7201435252897ff9f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:08.775792Z","signature_b64":"4NTEF7jBPNUlyNl78pzvBPwv2/SIA6xRhS/o4SIGbf3rtreKQg0Rvg/WTVM26xPXFDXmyINbjMqneCiNhdFfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d02d11b8ded4b8650a887a109176dcd20b21828e40a6a89e459da03db9593f08","last_reissued_at":"2026-05-18T02:41:08.775265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:08.775265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maps between certain complex Grassmann manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Parameswaran Sankaran, Prateep Chakraborty","submitted_at":"2013-12-17T12:21:22Z","abstract_excerpt":"Let $k,l,m,n$ be positive integers such that $m-l\\ge l>k, m-l>n-k\\ge k$ and $m-l>2k^2-k-1$. 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