Maurer-Cartan moduli and models for function spaces

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.

22 pages. This version, which will appear in Advances in Mathematics, contains various technical corrections and updated bibliography

References in corpus (4)

• Deformation theory and rational homotopy type
• Cohomology theories for homotopy algebras and noncommutative geometry
• Rational homotopy theory of mapping spaces via Lie theory for L-infinity algebras
• L-infinity maps and twistings