{"paper":{"title":"On the Hurewicz homomorphism on the extensions of ideals in $\\pi_*^s$ and spherical classes in $H_*Q_0S^0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hadi Zare","submitted_at":"2015-04-25T19:04:14Z","abstract_excerpt":"This is about Curtis conjecture on the image of the Hurewicz map $h:{_2\\pi_*}Q_0S^0\\to H_*(Q_0S^0;\\Z/2)$. First, we show that if $f\\in{_2\\pi_*^s}$ is of Adams filtration at least $3$ with $h(f)\\neq 0$ then $f$ is not a decomposable element in ${_2\\pi_*^s}$. Moreover, it is shown if $k$ is the least positive integer that $f$ is represented by a cycle in $\\mathrm{Ext}^{k,k+n}_A(\\Z/2,\\Z/2)$, then (i) if $e_*h(f)\\neq 0$ then $n\\geqslant 2^k-1$; (ii) if $e_*h(f)=0$ then $n\\geqslant 2^k-2^t$ for some $t>1$. Second, for $S\\subseteq{_2\\pi_{*>0}^s}$ we show that: (i) if the conjecture holds on $S$, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06752","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"}