A splitting theorem for holomorphic Banach bundles

2008/05/14 by Jaehong Kim, Kim, Jaehong
Mathematics · #32L05 #32L10 #58B15 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32L05 #msc:32L10 #msc:58B15

paper · pdf · doi:10.48550/arxiv.0805.1953

arxiv created 2008/05/14 · arxiv updated 2009/12/01

Abstract

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 → 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 H¹(X, Ø)=0.

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