{"paper":{"title":"Weak equivalence classes of complex vector bundles","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Hong-Van Le","submitted_at":"2006-09-03T08:55:33Z","abstract_excerpt":"For any complex vector bundle $E^k$ of rank $k$ over a manifold $M^m$ with Chern classes $c_i \\in H^{2i}(M^m,\\Z)$ and any non-negative integers $l_1, >..., l_k$ we show the existence of a positive number $N(k,m)$ and the existence of a complex vector bundle $\\hat E^k$ over $M^m$ whose Chern classes are $ N(k,m) \\cdot l_i\\cdot c_i\\in H^{2i} (M^m,\\Z)$. We also discuss a version of this statement for holomorphic vector bundles over projective algebraic manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609074","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"}