Holomorphic Banach bundles over compact manifolds
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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