{"paper":{"title":"Fr\\\"olicher-Nijenhuis bracket on manifolds with special holonomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"H\\^ong V\\^an L\\^e, Kotaro Kawai, Lorenz Schwachh\\\"ofer","submitted_at":"2018-10-30T13:09:27Z","abstract_excerpt":"In this article, we summarize our recent results on the study of manifolds with special holonomy via the Fr\\\"olicher-Nijenhuis bracket. This bracket enables us to define the Fr\\\"olicher-Nijenhuis cohomologies which are analogues of the $d^c$ and the Dolbeault cohomologies in K\\\"ahler geometry, and assigns an $L_\\infty$-algebra to each associative submanifold. We provide several concrete computations of the Fr\\\"olicher-Nijenhuis cohomology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12714","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"}