The transport Oka-Grauert principle for simple surfaces

I will explain how to show the existence of matrix holomorphic integrating factors on simple surfaces and how this gives rise to a full description of the range of the non-Abelian X-ray transform. The main result can be recast as the absence of non-trivial holomorphic vector bundles over the twistor space of a simple surface thus providing a transport version of the classical Oka-Grauert principle in complex geometry. This is joint work with Jan Bohr.

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