{"paper":{"title":"The mod-$p$ homology of the classifying spaces of certain gauge groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Daisuke Kishimoto, Stephen Theriault","submitted_at":"2018-10-10T23:04:49Z","abstract_excerpt":"Let $G$ be a simply-connected, simple compact Lie group of type $\\{n_{1},\\ldots,n_{\\ell}\\}$, where $n_{1}\\le\\cdots \\le n_{\\ell}$. Let $\\mathcal{G}_k$ be the gauge group of the principal $G$-bundle (namedright{P}{}{S^{4}}) whose isomorphism class is determined by the the second Chern class having value $k\\in\\mathbb{Z}$. We calculate the mod-$p$ homology of the classifying space $B\\mathcal{G}_k$ provided that $n_{\\ell}<p-1$ and $p$ does not divide $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04771","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.04771/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}