{"paper":{"title":"Tractor calculus, BGG complexes, and the cohomology of Kleinian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.DG","authors_text":"A.Rod Gover, Callum Sleigh","submitted_at":"2014-12-02T06:29:34Z","abstract_excerpt":"For a compact, oriented, hyperbolic $n$-manifold $(M,g)$, realised as $M= \\Gamma \\backslash \\mathbb{H}^{n}$ where $\\Gamma$ is a torsion-free cocompact subgroup of $SO(n,1)$, we establish and study a relationship between differential geometric cohomology on $M$ and algebraic invariants of the group $\\Gamma$. In particular for $\\mathbb{F}$ an irreducible $SO(n,1)$-module, we show that the group cohomology with coefficients $H^{\\bullet}(\\Gamma, \\mathbb{F})$ is isomorphic to the cohomology of an appropriate projective BGG complex on $M$. This yields the geometric interpretation that $H^{\\bullet}(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0792","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"}