{"paper":{"title":"Exponents of $[\\Omega(\\mathbb S^{r+1}), \\Omega (Y)]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Daciberg Lima Gon\\c{c}alves, Marek Golasi\\'nski, Peter Wong","submitted_at":"2018-09-26T00:38:04Z","abstract_excerpt":"We investigate the exponents of the total Cohen groups $[\\Omega(\\mathbb S^{r+1}), \\Omega(Y)]$ for any $r\\ge 1$. In particular, we show that for $p\\ge 3$, the $p$-primary exponents of $[\\Omega(\\mathbb S^{r+1}), \\Omega(\\mathbb S^{2n+1})]$ and $[\\Omega(\\mathbb S^{r+1}), \\Omega(\\mathbb S^{2n})]$ coincide with the $p$-primary homotopy exponents of spheres $\\mathbb S^{2n+1}$ and $\\mathbb S^{2n}$, respectively.\n  We further study the exponent problem when $Y$ is a space with the homotopy type of $\\Sigma(n)/G$ for a homotopy $n$-sphere $\\Sigma(n)$, the complex projective space $\\mathbb{C}P^n$ for $n\\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09768","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"}