{"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 $m-l>2k^2-k-1$. Let $G_{k}(\\mathbb{C}^n)$ denote the Grassmann manifold of $k$-dimensional vector subspaces of $\\bc^n$. We show that any continuous map $f:G_{l}(\\bc^m)\\to G_{k}(\\mathbb{C}^n)$ is rationally null-homotopic. 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 $\\mathbb{C}^m\\cong \\bc^n\\oplus\\bc^{m-n}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4743","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"}