#### Volume 19, issue 3 (2019)

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Representing the deformation $\infty$–groupoid

### Daniel Robert-Nicoud

Algebraic & Geometric Topology 19 (2019) 1453–1476
##### Abstract

Our goal is to introduce a smaller, but equivalent version of the deformation $\infty$–groupoid associated to a homotopy Lie algebra. In the case of differential graded Lie algebras, we represent it by a universal cosimplicial object.

##### Keywords
deformation theory, Deligne groupoid, differential graded Lie algebras, Maurer–Cartan elements
##### Mathematical Subject Classification 2010
Primary: 17B55
Secondary: 18G55, 55U10