On the classification of complex vector bundles of stable rank

Details On the classification of complex vector bundles of stable rank On the classification of complex vector bundles of stable rank

2006-09-11

arxiv.org/abs/math/0609282v1

Proc. Indian Acad, Sci. vol. 116 (3), 2006, 271-291

Mathematics

Algebraic Geometry

21 pages; The work was completed in 1990, and circulated as a Goettingen preprint Heft 5 (1991). Also, the main results were a

Scientific paper

One describes, using a detailed analysis of Atiyah--Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe in constructive terms the Chern classes of a vector bundle.

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