{"paper":{"title":"Realizing homotopy group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"David Blanc, Debasis Sen","submitted_at":"2012-10-09T11:57:23Z","abstract_excerpt":"For any finite group $G$, we define the notion of a Bredon homotopy action of $G$, modelled on the diagram of fixed point sets $(X_H)_{H\\leq G}$ for a $G$-space $X$, together with a pointed homotopy action of the group $N_{G}H/H$ on $X^{H}/(\\bigcup_{H<K} X^{K})$. We then describe a procedure for constructing a suitable diagram $\\underline{X}:O_G^{op}\\to Top$ from this data, by solving a sequence of elementary lifting problems. If successful, we obtain a $G$-space $X'$ realizing the given homotopy information, determined up to Bredon $G$-homotopy type. Such lifting methods may also be used to u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2574","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"}