Holomorphic Banach bundles over compact manifolds

Jaehong Kim, Purdue University

Abstract

This thesis 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,[special characters omitted]) = 0.

Degree

Ph.D.

Advisors

Lempert, Purdue University.

Subject Area

Mathematics

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