{"paper":{"title":"Certain maps preserving self-homotopy equivalences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jin-ho Lee, Toshihiro Yamaguchi","submitted_at":"2015-06-30T15:42:17Z","abstract_excerpt":"Let $\\mathcal{E}(X)$ be the group of homotopy classes of self homotopy equivalences for a connected CW complex $X$. We observe two classes of maps $\\mathcal{E}$-maps and co-$\\mathcal{E}$-maps. They are defined as the maps $X\\to Y$ that induce the homomorphisms $\\mathcal{E}(X)\\to \\mathcal{E}( Y)$ and $\\mathcal{E}(Y)\\to \\mathcal{E}(X)$, respectively. We give some rationalized examples related to spheres, Lie groups and homogeneous spaces by using Sullivan models. Furthermore, we introduce an $\\mathcal{E}$-equivalence relation between rationalized spaces $X_{\\mathbb{Q}}$ and $Y_{\\mathbb{Q}}$ as a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.09126","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"}