{"paper":{"title":"The squaring operartion and the Singer algebraic transfer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nguyen Sum","submitted_at":"2016-09-10T06:30:00Z","abstract_excerpt":"Let $P_k$ be the graded polynomial algebra $\\mathbb F_2[x_1,x_2,\\ldots ,x_k]$, with the degree of each $x_i$ being 1, regarded as a module over the mod-2 Steenrod algebra $\\mathcal A$, and let $GL_k$ be the general linear group over the prime field $\\mathbb F_2$ which acts regularly on $P_k$. We study the algebraic transfer constructed by Singer using the technique of the hit problem. This transfer is a homomorphism from the homology of the mod-2 Steenrod algebra, $\\text{Tor}^{\\mathcal A}_{k,k+n} (\\mathbb F_2,\\mathbb F_2)$, to the subspace of $\\mathbb F_2{\\otimes}_{\\mathcal A}P_k$ consisting o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03006","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"}