{"paper":{"title":"Rank Constrained Homotopies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.OA","authors_text":"Kaushika De Silva","submitted_at":"2015-11-20T18:42:07Z","abstract_excerpt":"For any $n\\geq k\\geq l\\in\\mathbb{N},$ let $S(n,k,l)$ be the set of all those non-negative definite matrices $a\\in M_{n}(\\mathbb{C})$ with $l\\leq\\text{rank }a\\leq k$. Motivated by applications to $C^{*}$-algebra theory, we investigate the homotopy properties of continuous maps from a compact Hausdorff space $X$ into sets of the form $S(n,k,l).$ It is known that for any $n,$ if $k-l$ is approximately 4 times the covering dimension of $X$ then there is only one homotopy class of maps from $X$ into $S(n,k,l)$, i.e. $C(X,S(n,k,l))$ is path connected. In our main Theorem we improve this bound by a f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06723","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"}