{"paper":{"title":"The secondary periodic element $\\beta_{p^2/p^2-1}$ and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jianguo Hong, Xiangjun Wang","submitted_at":"2014-02-25T07:39:58Z","abstract_excerpt":"In this paper we prove that $\\beta_{p^2/p^2-1}$ survives to $E_\\infty$ in the Adams-Novikov spectral sequence for $p\\geqslant 5$. As an easy consequence we prove that $\\beta_{sp^2/j}$ are perminent cycles for all $s\\geqslant 1$, $j\\leqslant p^2-1$. From the Thom map $\\Phi: Ext^{s,t}_{BP_*BP}(BP_*, BP_*)\\longrightarrow Ext^{s,t}_A(\\mathbb{Z}/p, \\mathbb{Z}/p)$, we also see that $h_0h_3$ survives to $E_\\infty$ in the classical Adams spectral sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6074","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"}