{"paper":{"title":"Topology of polyhedral products over simplicial multiwedges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ivan Limonchenko","submitted_at":"2017-11-01T17:57:15Z","abstract_excerpt":"We prove that certain conditions on multigraded Betti numbers of a simplicial complex $K$ imply existence of a higher Massey product in cohomology of a moment-angle-complex $\\mathcal Z_K$, which contains a unique element (a strictly defined product). Using the simplicial multiwedge construction, we find a family $\\mathcal{F}$ of polyhedral products being smooth closed manifolds such that for any $l,r\\geq 2$ there exists an $l$-connected manifold $M\\in\\mathcal F$ with a nontrivial strictly defined $r$-fold Massey product in $H^{*}(M)$. As an application to homological algebra, we determine a wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00461","kind":"arxiv","version":2},"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"}