Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
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.