A splitting theorem for holomorphic Banach bundles

Details A splitting theorem for holomorphic Banach bundles A splitting theorem for holomorphic Banach bundles

2008-05-14

arxiv.org/abs/0805.1953v1

Mathematics

Complex Variables

Scientific paper

This paper is motivated by Grothendieck's splitting theorem. In the 1960s, Gohberg generalized this to a class of Banach bundles. We consider a compact complex manifold $X$ and a holomorphic Banach bundle $E \to X$ that is a compact perturbation of a trivial bundle in a sense recently introduced by Lempert. We prove that $E$ splits into the sum of a finite rank bundle and a trivial bundle, provided $H^{1}(X, \O)=0$.

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