Semicosimplicial DGLAs in deformation theory
Domenico Fiorenza, Marco Manetti, Elena Martinengo
TL;DR
This paper connects Cech cocycles in nonabelian group cohomology with Maurer-Cartan elements in L-infinity algebras, providing new tools for deformation theory analysis.
Contribution
It introduces a novel identification between Cech cocycles and Maurer-Cartan elements within a specific L-infinity algebra framework.
Findings
Establishes a correspondence between nonabelian cohomology and Maurer-Cartan elements.
Provides applications of this correspondence to deformation theory.
Enhances understanding of deformation problems via semicosimplicial DGLAs.
Abstract
We identify Cech cocycles in nonabelian (formal) group cohomology with Maurer-Cartan elements in a suitable L-infinity algebra. Applications to deformation theory are described.
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