p. 23 - 30 Weak equivalence classes of complex vector bundles Hông-Vân Lê 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. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |