Maurer–Cartan moduli and models for function spaces

Lazarev, Andrey (2013) Maurer–Cartan moduli and models for function spaces. Advances in Mathematics, 235. pp. 296-320. ISSN 0001-8708

Abstract

We set up a formalism of Maurer–Cartan moduli sets for L∞ 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.