{"paper":{"title":"Detection of some elements in the stable homotopy groups of spheres","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Xiugui Liu","submitted_at":"2009-11-06T20:24:09Z","abstract_excerpt":"In this paper we constructs a new nontrivial family in the stable homotopy groups of spheres $\\pi_{p^nq+2pq+q-3}S$ which is of order $p$ and is represented by $k_0h_{n} \\in Ext_A^{3,p^nq+2pq+q}(\\mathbb{Z}_p,\\mathbb{Z}_p)$ in the Adams spectral sequence, where $p\\geq 5$ is an odd prime, $n\\geq 3$ and $q=2(p-1)$. In the course of the proof, a new family of homotopy elements in $\\pi_{\\ast}V(1)$ which is represented by $\\beta_{\\ast}{i^{\\prime}}_{\\ast}i_{\\ast}({h}_n)\\in Ext_A^{2,p^nq+(p+1)q+1}(H^{\\ast}V(1),\\mathbb{Z}_p)$ in the Adams sequence is detected."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1344","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"}