{"paper":{"title":"Realizability of the group of rational self-homotopy equivalences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Mahmoud Benkhalifa","submitted_at":"2010-10-07T14:24:19Z","abstract_excerpt":"For a 1-connected CW-complex $X$, let $\\mathcal{E}(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$. The aim of this paper is to prove that, for every $n\\in\\Bbb N$, there exists a 1-connected rational CW-complex $X_{n}$ such that $\\mathcal{E}(X_{n})\\cong \\underset{2^{n+1}\\mathrm{. times}}{\\underbrace{\\Bbb Z_{2}\\oplus... \\Bbb \\oplus \\Bbb Z_{2}}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1441","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"}