{"paper":{"title":"Topology of the octonionic flag manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AT","authors_text":"Augustin-Liviu Mare, Matthieu Willems","submitted_at":"2008-09-25T04:12:51Z","abstract_excerpt":"The octonionic flag manifold $Fl(\\mathbb{O})$ is the space of all pairs in $\\mathbb{O}P^2\\times \\mathbb{O}P^2$ (where $\\mathbb{O}P^2$ denotes the octonionic projective plane) which satisfy a certain \"incidence\" relation. It comes equipped with the projections $\\pi_1,\\pi_2 : Fl(\\mathbb{O})\\to \\mathbb{O}P^2$, which are $\\mathbb{O}P^1$ bundles, as well as with an action of the group $Spin(8)$. The first two results of this paper give Borel type descriptions of the usual, respectively $Spin(8)$-equivariant cohomology of $Fl(\\mathbb{O})$ in terms of $\\pi_1$ and $\\pi_2$ (actually the Euler classes o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4318","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"}