{"paper":{"title":"Higher cohomology for Anosov actions on certain homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Felipe A. Ramirez","submitted_at":"2011-07-23T13:34:10Z","abstract_excerpt":"We study the smooth untwisted cohomology with real coefficients for the action on [SL(2, R) \\times \\cdot \\cdot \\cdot \\times SL(2, R)]/{\\Gamma} by the subgroup of diagonal matrices, where {\\Gamma} is an irreducible lattice. In the top degree, we show that the obstructions to solving the coboundary equation come from distributions that are invariant under the action. In intermediate degrees, we show that the cohomology trivializes. It has been conjectured by A. and S. Katok that, for a standard partially hyperbolic R^d- or Z^d-action, the obstructions to solving the top-degree coboundary equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4689","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"}