Geodesic
Weak equivalence classes of complex vector bundles
Acta mathematica Universitatis Comenianae, Tome 77 (2008) no. 1 
Hông-Vân Lê. Weak equivalence classes of complex vector bundles. Acta mathematica Universitatis Comenianae, Tome 77 (2008) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2008_77_1_a2/
@article{AMUC_2008_77_1_a2,
     author = {H\^ong-V\^an L\^e},
     title = {Weak equivalence classes of complex vector bundles},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2008},
     volume = {77},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2008_77_1_a2/}
}
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Voir la notice de l'article provenant de la source Comenius University

For any complex vector bundle E k of rank k over a manifold M m with Chern classes ci Î H 2i ( M m, Z ) and any non-negative integers l 1 , . . ., lk we show the existence of a positive number p ( m, k ) and the existence of a complex vector bundle Ê k over M m whose Chern classes are p ( m, k ) × li × ci Î H 2i ( Mm, Z ). We also discuss a version of this statement for holomorphic vector bundles over projective algebraic manifolds.