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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
Aug 24, 2006
Published:
Aug 24, 2006
MSC Codes:
53C10, 53C42, 55R25, 55R37
Keywords:
chern class, complex Grassmannian, weak equivalence

Related publications

inJournal
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