{"paper":{"title":"Immersions in a Quaternionic Grassmannian inducing a given 4-form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mahuya Datta","submitted_at":"2012-12-24T09:59:13Z","abstract_excerpt":"Let $Gr_k(\\H^n)$ be the Grassmannian manifold of Quaternionic $k$-planes in $\\H^n$ and let $\\gamma^n_k\\to Gr_k(\\H^n)$ denote the Stiefel bundle of quaternionic $k$-frames in $\\H^n$. Let $\\sigma$ denote the first symplectic Pontrjagin form associated with the universal connection on $\\gamma^n_k$. We show that every 4-form $\\omega$ on a smooth manifold $M$ can be induced from $\\sigma$ by a smooth immersion $f:M\\to Gr_k(\\H^n)$ (for sufficiently large $k$ and $n$) provided there exists a continuous map $f_0:M\\to Gr_k(\\H^n)$ which pulls back the cohomology class of $\\sigma$ onto that of $\\omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5885","kind":"arxiv","version":1},"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"}