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arxiv: math/0609074 · v1 · pith:RRRXQE5Hnew · submitted 2006-09-03 · 🧮 math.DG · math.AT

Weak equivalence classes of complex vector bundles

classification 🧮 math.DG math.AT
keywords vectorclassescomplexbundlebundlescdotchernexistence
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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.

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