{"paper":{"title":"Spheroidal groups, virtual cohomology and lower dimensional G-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AT","authors_text":"William Browder","submitted_at":"2016-05-08T23:27:42Z","abstract_excerpt":"A space is defined to be \"$n$-spheroidal\" if it has the homotopy type of an $n$-dimensional CW-complex $X$ with $H_{n}(X, \\mathbb{Z})$ not zero and finitely generated. A group $G$ is called \"$n$-spheroidal\" if its classifying space $K(G,1)$ is $n$-spheroidal. Examples include fundamental groups of compact manifold $K(G,1)$'s. Moreover, the class of groups $G$ which are $n$-spheroidal for some $n$, is closed under products, free products, and group extensions. If $Y$ is a space with $\\pi_{1}(Y)$ $n$-spheroidal, and if $H_{k}(Y;\\mathbb{F}_{p})$ is non-zero and finitely generated, and if $H_{i}(Y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02387","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"}