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MiS Preprint

Weak equivalence classes of complex vector bundles

Hông Vân Lê


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.

MSC Codes:
53C10, 53C42, 55R25, 55R37
chern class, complex Grassmannian, weak equivalence

Related publications

2008 Journal Open Access
Hông Vân Lê

Weak equivalence classes of complex vector bundles

In: Acta mathematica Universitatis Comenianae, 77 (2008) 1, pp. 23-30