Weak equivalence classes of complex vector bundles

Details Weak equivalence classes of complex vector bundles Weak equivalence classes of complex vector bundles

2006-09-03

arxiv.org/abs/math/0609074v1

Acta Mathematica Univ. Comenianae, vol 77, N1, (2008), 23-30

Mathematics

Differential Geometry

This note contains also a new full proof of Proposition 2.7 of my previous note "Realizing homology classes by symplectic subm

Scientific paper

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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