{"paper":{"title":"On the realizability of group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AT","authors_text":"Antonio Viruel, Cristina Costoya","submitted_at":"2015-11-19T19:37:26Z","abstract_excerpt":"We raise the question of realizability of group actions which is an extended version of the 1960's Kahn realizability problem for (abstract) groups. Namely, if $M$ is a $\\mathbb ZG$-module for a group $G$, we say that a simply-connected space $X$ realize this action if, for some $k$, $\\pi_k(X)$ as a $\\mathbb Z \\mathcal E (X) $-module for the group $\\mathcal E (X)$ of self-homotopy equivalences of $X$, is isomorphic to $M$ as a $\\mathbb ZG$-module. Which modules can be so realized? In this paper we obtain a positive answer for any faithful finitely generated $\\mathbb Q G$-module, where $G$ is f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06322","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"}