{"paper":{"title":"Aspherical completions and rationally inert elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Steve Halperin, Yves Felix","submitted_at":"2019-04-18T12:03:57Z","abstract_excerpt":"Let $X$ be a connected space. An element $[f]\\in \\pi_n(X)$ is called rationally inert if\n  $\\pi_*(X)\\otimes \\mathbb Q \\to \\pi_*(X\\cup_fD^{n+1})\\otimes \\mathbb Q$ is surjective. We extend the results obtained in the simply connected case, and prove in particular that if $X\\cup_fD^{n+1}$ is a Poincar\\'e duality complex and the algebra $H(X)$ requires at least two generators then $[f]\\in \\pi_n(X)$ is rationally inert. On the other hand, if $X$ is rationally a wedge of at least two spheres and $f$ is rationally non trivial, then $f$ is rationally inert. Finally if $f$ is rationally inert then the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08714","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"}