### The nerve of a differential graded algebra

**Getzler, E ***(Northwestern University)*

Friday 05 April 2013, 09:30-10:30

Seminar Room 1, Newton Institute

#### Abstract

The nerve of a differential graded algebra is a quasicategory: in this talk, we explain what the quasi-iso-morphisms look like in this quasicategory. If the dg algebra A is a dg Banach algebra concentrated in dimensions i>-n , the nerve of A is a Lie n-stack, that is, a quasicategory enriched in Banach analytic spaces. We show that Kuranishi's approach yields a finite dimensional Lie n-stack parametrizing deformations of a complex of holomorphic vector bundles on a compact complex manifold of length n. This is joint work with Kai Behrend.

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