{"paper":{"title":"Recovering trees from the cohomology ring of their configuration spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Teresa I. Hoekstra-Mendoza","submitted_at":"2023-12-27T17:23:18Z","abstract_excerpt":"Given a tree $T$, the cohomology ring of its unordered configuration space $H^{\\ast}(U\\mathcal{D}^nT)$ is an exterior face algebra if $T$ is a binary core tree (if by removing the leaves from $T$ we obtain a binary tree), or if $n=4$. This means that every cup product is determined by a simplicial complex $K_nT$. In this paper we show how to recover the tree $T$ from the simplicial complex $K_nT$ when $n=4.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16646","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.16646/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}