Maurer-Cartan moduli and models for function spaces

TL;DR

This paper develops a formalism for Maurer-Cartan moduli sets in L-infinity algebras, enabling homotopy-invariant models for function spaces and advancing rational homotopy theory.

Contribution

It introduces a new formalism based on closed model categories to study Maurer-Cartan moduli and constructs rational models for function spaces.

Findings

Homotopy-invariant treatment of Chevalley-Eilenberg and Harrison cohomology

Construction of rational homotopy models for function spaces

Formalism based on differential graded coalgebras

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.