{"paper":{"title":"On the image of the unstable Boardman map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hadi Zare","submitted_at":"2018-06-19T07:32:06Z","abstract_excerpt":"We consider the `unstable Boardman map' (homomorphism if $k>0$) $$b:\\pi^{m+k}\\Sigma^k\\Omega^lS^{n+l}\\simeq[\\Omega^lS^{n+l},\\Omega^kS^{m+k}]\\longrightarrow \\mathrm{Hom}(H_*\\Omega^lS^{n+l},H_*\\Omega^kS^{m+k})$$ defined by $h(f)=f_*$. We work at the prime $2$, with $k=0$, and determine the image for various in the following cases : (1) $m=n$ and $l>0$ arbitrary; (2) $m>n$ and $l=1$. We observe that in most of the cases the image is trivial with the exceptions corresponding to the cases when either there is a (commutative) $H$-space structure on $S^n$ or there is a Hopf invariant one element."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07079","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"}