{"paper":{"title":"The homotopy type of skeleta of the flag complex over a finite vector space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jesus Gonzalez, Jorge Aguilar-Guzman, Jose Luis Leon-Medina","submitted_at":"2018-10-09T21:18:10Z","abstract_excerpt":"The aim of this paper is to give a (discrete) Morse theoretic proof of the fact that the $k$-th skeleton of the flag complex $\\mathcal{F}$, associated to the lattice of subspaces of a finite dimensional vector space, is homotopy equivalent to a wedge of spheres of dimension $\\min\\{k,\\dim(\\mathcal{F})\\}$. The tight control provided by Morse theoretic methods allows us to give an explicit formula for the number of spheres appearing in each of these wedge summands."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04248","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"}