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MiS Preprint
87/2006
Weak equivalence classes of complex vector bundles
Hông Vân Lê
Abstract
For any complex vector bundle $E^k$ of rank $k$ over a manifold $M^m$ with the Chern classes $c_i \in H^{2i}(M^m,Z)$ and any non-negative integers $l_1, \cdots, l_k$ we show the existence of a positive number $N(k,m)$ and the existence of a 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 $E^k$ over projective algebraic manifolds.
