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Weak equivalence classes of complex vector bundles
Received: August 30, 2006; Accepted: December 04, 2006
Abstract. 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.
Keywords: Chern classes; complex Grassmannians; weak equivalence.
AMS Subject classification: Primary: 55R25; 55R37.
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