{"paper":{"title":"Equivariant Moore spaces and the Dade group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ergun Yalcin","submitted_at":"2016-06-11T15:25:39Z","abstract_excerpt":"Let $G$ be a finite $p$-group and $k$ be a field of characteristic $p$. A topological space $X$ is called an $n$-Moore space if its reduced homology is nonzero only in dimension $n$. We call a $G$-CW-complex $X$ an $\\underline{n}$-Moore $G$-space over $k$ if for every subgroup $H$ of $G$, the fixed point set $X^H$ is an $\\underline{n}(H)$-Moore space with coefficients in $k$, where $\\underline{n}(H)$ is a function of $H$. We show that if $X$ is a finite $\\underline{n}$-Moore $G$-space, then the reduced homology module of $X$ is an endo-permutation $kG$-module generated by relative syzygies. A "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03607","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"}