{"paper":{"title":"Relations among the kernels and images of {S}teenrod squares acting on right $\\mathcal{A}$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Shaun V. Ault","submitted_at":"2011-06-15T16:06:34Z","abstract_excerpt":"In this note, we examine the right action of the Steenrod algebra $\\mathcal{A}$ on the homology groups $H_*(BV_s, \\F_2)$, where $V_s = \\F_2^s$. We find a relationship between the intersection of kernels of $Sq^{2^i}$ and the intersection of images of $Sq^{2^{i+1}-1}$, which can be generalized to arbitrary right $\\mathcal{A}$-modules. While it is easy to show that $\\bigcap_{i=0}^{k} \\mathrm{im}\\,Sq^{2^{i+1}-1} \\subseteq \\bigcap_{i = 0}^k \\mathrm{ker}\\,Sq^{2^i}$ for any given $k \\geq 0$, the reverse inclusion need not be true. We develop the machinery of homotopy systems and null subspaces in or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3012","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"}