{"paper":{"title":"A vanishing theorem for the homology of discrete subgroups of $\\mathrm{Sp}(n,1)$ and $\\mathrm{F}_4^{-20}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.GT","authors_text":"Benson Farb, Chris Connell, D. B. McReynolds","submitted_at":"2015-06-11T00:35:54Z","abstract_excerpt":"For any discrete, torsion-free subgroup $\\Gamma$ of $\\mathrm{Sp}(n,1)$ (resp.\\ $\\mathrm{F}_4^{-20}$) with no parabolic elements, we prove that $H_{4n-1}(\\Gamma;V)=0$ (resp.\\ $H_i(\\Gamma;V)=0$ for $i=13,14,15$) for any $\\Gamma$--module $V$. The main technical advance is a new bound on the $p$--Jacobian of the barycenter map of Besson--Courtois--Gallot. We also apply this estimate to obtain an inequality between the critical exponent and homological dimension of $\\Gamma$, improving on work of M.~Kapovich."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03516","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":""},"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"}