{"paper":{"title":"Mapping spaces from projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Mitsunobu Tsutaya","submitted_at":"2014-08-09T02:52:09Z","abstract_excerpt":"We denote the $n$-th projective space of a topological monoid $G$ by $B_nG$ and the classifying space by $BG$. Let $G$ be a well-pointed topological monoid of the homotopy type of a CW complex and $G'$ a well-pointed grouplike topological monoid. We prove the weak equivalence between the pointed mapping space $\\mathrm{Map}_0(B_nG,BG)$ and the space of all $A_n$-maps from $G$ to $G'$. This fact has several applications. As the first application, we show that the connecting map $G\\rightarrow\\mathrm{Map}_0(B_nG,BG)$ of the evaluation fiber sequence $\\mathrm{Map}_0(B_nG,BG)\\rightarrow\\mathrm{Map}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2010","kind":"arxiv","version":4},"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"}