{"paper":{"title":"On Freudenthal theorem, Kahn-Priddy Theorem, and Curits conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hadi Zare","submitted_at":"2018-01-23T10:53:17Z","abstract_excerpt":"We verify Curtis conjecture on a class of elements of ${_2\\pi_*^s}$ that satisfy a certain factorisation property. To be more precise, suppose $f\\in{_2\\pi_n^s}$ pulls back to $g\\in{_2\\pi_n^s}P$ through the Kahn-Priddy map $\\lambda:QP\\to Q_0S^0$ such that $g$ projects nontrivially to an element $g'\\in{_2\\pi_n^s}P_{t(n)}$ with $h(g')=0$ where $h:{_2\\pi_*}QP_k\\to H_*QP_k$ is the unstable Hurewicz map, and $t(n)=\\lceil n/2\\rceil$. Then, mod out by elements of ${_2\\pi_*^s}\\simeq{_2\\pi_*}QS^0$ satisfying this property, the Curtis conjecture on the image of $h:{_2\\pi_*}QS^0\\to H_*QS^0$ holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07480","kind":"arxiv","version":3},"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"}