## Higher analytic stacks

### Ezra Getzler – 19 August 2011

(joint with Kai Behrend) The invertible elements of a Banach algebra form a Lie group. There is a generalization of this observation to differential graded Banach algebras, in which the quasi-invertible elements form the morphisms of an n-groupoid in the category of analytic Banach varieties. I will explain how this observation forms the basis for a generalization of Kuranishi's work on deformation of holomorphic vector bundles to perfect complexes (bounded complexes of
holomorphic vector bundles).

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