{"paper":{"title":"2-associahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.SG","authors_text":"Nathaniel Bottman","submitted_at":"2017-09-01T00:49:08Z","abstract_excerpt":"For any $r\\geq 1$ and $\\mathbf{n} \\in \\mathbb{Z}_{\\geq0}^r \\setminus \\{\\mathbf0\\}$ we construct a poset $W_{\\mathbf{n}}$ called a 2-associahedron. The 2-associahedra arose in symplectic geometry, where they are expected to control maps between Fukaya categories of different symplectic manifolds. We prove that the completion $\\widehat{W_{\\mathbf{n}}}$ is an abstract polytope of dimension $|\\mathbf{n}|+r-3$. There are forgetful maps $W_{\\mathbf{n}} \\to K_r$, where $K_r$ is the $(r-2)$-dimensional associahedron, and the 2-associahedra specialize to the associahedra (in two ways) and to the multip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00119","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"}