{"paper":{"title":"Brown's Criterion and classifying spaces for families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Eduardo Mart\\'inez-Pedroza, Luis Jorge S\\'anchez Salda\\~na","submitted_at":"2019-08-15T13:52:39Z","abstract_excerpt":"Let $G$ be a group and $\\mathcal{F}$ be a family of subgroups closed under conjugation and subgroups. A model for the classifying space $E_{\\mathcal{F}} G$ is a $G$-CW-complex $X$ such that every isotropy group belongs to $\\mathcal{F}$, and for all $H\\in \\mathcal{F}$ the fixed point subspace $X^H$ is contractible. The group $G$ is of type $\\mathcal{F}\\text{-}\\mathrm{F}_{n}$ if it admits a model for $E_\\mathcal{F} G$ with $n$-skeleton with compact orbit space. The main result of the article provides is a characterization of $\\mathcal{F}\\text{-}\\mathrm{F}_{n}$ analogue to Brown's criterion for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05543","kind":"arxiv","version":3},"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/1908.05543/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"}