Representing the deformation $\infty$-groupoid

Abstract

The goal of the present paper is to introduce a smaller, but equivalent version of the Deligne-Hinich-Getzler $\infty$-groupoid associated to a homotopy Lie algebra. In the case of differential graded Lie algebras, we represent it by a universal cosimplicial object.

13 pages; (v2): changes in Section 4, small changes throughout the text and updated references; (v3): updated title and bibliography, corrected some typos, and minor corrections; in particular, fixed a minor error in Prop. 4.1

References in corpus (3)

• Pre-Lie deformation theory
• Higher Lie theory
• Deformation theory with homotopy algebra structures on tensor products

Cited by in corpus (9)

• Deformation theory of Cohomological Field Theories
• Descent of Deligne-Getzler $\infty$-groupoids
• The infinity Quillen functor, Maurer-Cartan elements and DGL realizations
• Mirrors, Functoriality, and Derived Geometry
• Convolution algebras and the deformation theory of infinity-morphisms
• A model structure for the Goldman-Millson theorem
• Higher structures in rational homotopy theory
• Spatial realization of a Lie algebra and Bar construction of a group
• All known realizations of complete Lie algebras coincide