{"paper":{"title":"Iterated doubles of the Joker and their realisability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andrew Baker","submitted_at":"2017-10-09T07:36:52Z","abstract_excerpt":"Let $\\mathcal{A}(1)^*$ be the subHopf algebra of the mod~$2$ Steenrod algebra $\\mathcal{A}^*$ generated by $\\mathrm{Sq}^1$ and $\\mathrm{Sq}^2$. The \\emph{Joker} is the cyclic $\\mathcal{A}(1)^*$-module $\\mathcal{A}(1)^*/\\mathcal{A}(1)^*\\{\\mathrm{Sq}^3\\}$ which plays a special r\\^ole in the study of $\\mathcal{A}(1)^*$-modules. We discuss realisations of the Joker both as an $\\mathcal{A}^*$-module and as the cohomology of a spectrum. We also consider analogous $\\mathcal{A}(n)^*$-modules for $n\\geq2$ and prove realisability results (both stable and unstable) for $n=2,3$ and non-realisability resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02974","kind":"arxiv","version":4},"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"}