{"paper":{"title":"The Fr\\\"olicher spectral sequence of certain solvmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.KT"],"primary_cat":"math.DG","authors_text":"Hisashi Kasuya","submitted_at":"2012-10-09T16:37:18Z","abstract_excerpt":"We show that the Fr\\\"olicher spectral sequence of a complex parallelizable solvmanifold is degenerate at $E_{2}$-term. For a semi-direct product $G=\\C^{n}\\ltimes_{\\phi}N$ of Lie-groups with lattice $\\Gamma=\\Gamma^{\\prime}\\ltimes \\Gamma^{\\prime\\prime}$ such that $N$ is a nilpotent Lie-group with a left-invariant complex structure and $\\phi$ is a semi-simple action, we also show that, if the Fr\\\"olicher spectral sequence of the nilmanifold $N/\\Gamma^{\\prime\\prime}$ is degenerate at $E_{r}$-term for $r\\ge 2$, then the Fr\\\"olicher spectral sequence of the solvmanifold $G/\\Gamma$ is also degenerate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2661","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"}