{"paper":{"title":"The effect of cell-attachment on the group of self-equivalences of an R-localized space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Mahmoud Benkhalifa, Samuel Bruce Smith","submitted_at":"2014-01-31T00:22:25Z","abstract_excerpt":"Let R be a subring of the rationals with least non-invertible prime p. Let X = X^{n} \\cup_{\\alpha} (\\bigcup_{j \\in J} e^{q}) be a cell attachment with J finite and q small with respect to p. Let E(X_R) denote the group of homotopy self-equivalences of the R-localization X_R. We use DG Lie models to construct a short exact sequence 0 \\to \\bigoplus_{j \\in J}\\pi_q(X^n)_R \\to E(X_R) \\to C^q \\to 0 where C^q is a subgroup of GL_{|J|}(R) \\times E(X^n_R). We obtain a related result for the R-localization of the nilpotent group E_*(X) of classes inducing the identity on homology. We deduce some explici"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8034","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"}