Maurer-Cartan moduli and models for function spaces

2011/09/16 by Lazarev, Andrey
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1109.3715

Abstract

We set up a formalism of Maurer-Cartan moduli sets for L-infinity algebras and associated twistings based on the closed model category structure on formal differential graded algebras (a.k.a. differential graded coalgebras). Among other things this formalism allows us to give a compact and manifestly homotopy invariant treatment of Chevalley-Eilenberg and Harrison cohomology. We apply the developed technology to construct rational homotopy models for function spaces.

Related

• Maurer-Cartan spaces of filtered L-infinity algebras
• Operads and Maurer-Cartan spaces
• Maurer-Cartan moduli and theorems of Riemann-Hilbert type
• Models for classifying spaces and derived deformation theory
• Derived deformation functors, Koszul duality, and Maurer-Cartan spaces