{"paper":{"title":"Some extensions in the Adams spectral sequence and the 51-stem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Guozhen Wang, Zhouli Xu","submitted_at":"2017-07-06T02:58:59Z","abstract_excerpt":"We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2-primary part of $\\pi_{51}$ is $\\mathbb{Z}/8\\oplus\\mathbb{Z}/8\\oplus\\mathbb{Z}/2$. This was the last unsolved 2-extension problem left by the recent works of Isaksen and the authors (\\cite{Isa1}, \\cite{IX}, \\cite{WX1}) through the 61-stem.\n  The proof of this result uses the $RP^\\infty$ technique, which was introduced by the authors in \\cite{WX1} to prove $\\pi_{61}=0$. This paper advertises this method through examples that have simpler proofs than in \\cite{WX1}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01620","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"}