{"paper":{"title":"On the stability of flat complex vector bundles over parallelizable manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Indranil Biswas, Manfred Lehn, Sorin Dumitrescu","submitted_at":"2017-09-18T14:06:21Z","abstract_excerpt":"We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds $G / \\Gamma$, where $G$ is a complex connected Lie group and $\\Gamma$ is a cocompact lattice in it. The main result proved here is a structure theorem for flat holomorphic vector bundles $E_\\rho$ associated to any irreducible representation $\\rho : \\Gamma \\rightarrow \\text{GL}(r,{\\mathbb C})$. More precisely, we prove that $E_{\\rho}$ is holomorphically isomorphic to a vector bundle of the form $E^{\\oplus n}$, where $E$ is a stable vector bundle. All the rational Chern classes of $E$ vanish, in part"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05951","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"}