{"paper":{"title":"Homotopy representations of the unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Krzysztof Ziemia\\'nski, Wojciech Lubawski","submitted_at":"2014-06-29T07:32:47Z","abstract_excerpt":"Let $G$ be a compact connected Lie group and let $\\xi,\\nu$ be complex vector bundles over the classifying space $BG$. The problem we consider is whether $\\xi$ contains a subbundle which is isomorphic to $\\nu$. The necessary condition is that for every prime $p$ the restriction $\\xi|_{BN_p^G}$, where $N_p^G$ is a maximal $p$-toral subgroup of $G$, contains a subbundle isomorphic to $\\nu|_{BN_p^G}$. We provide a criterion when this condition is sufficient, expressed in terms of $\\Lambda^*$-functors of Jackowski, McClure \\& Oliver and we prove that this criterion applies if $\\nu$ is a universal b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7467","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"}