{"paper":{"title":"C-symplectic poset structure on a simply connected space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Kazuya Hamada, Shoji Yokura, Toshihiro Yamaguchi","submitted_at":"2013-09-30T23:47:23Z","abstract_excerpt":"For a field $\\K$ of characteristic zero, we introduce a cohomologically symplectic poset structure ${\\mathcal P}_{\\K}(X)$ on a simply connected space $X$ from the viewpoint of $\\K$-homotopy theory. It is given by the poset of inclusions of subgroups preserving c-symplectic structures in the group ${\\mathcal E}(X_{\\K})$ of $\\K$-homotopy classes of $\\K$-homotopy self-equivalences of $X$, which is defined by the $\\K$-Sullivan model of $X$. We observe that the height of the Hasse diagram of ${\\mathcal P}_{\\K}(X)$ added by 1, denoted by c-s-${\\rm depth}_{\\K}(X)$, is finite and often depends on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0095","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"}