Andrey Lazarev (University of Leicester)
al179@leicester.ac.uk
We construct rational homotopy models for spaces of maps (continuous or smooth), where $X$ and $Y$ are topological spaces or manifolds satisfying some mild technical conditions. The result is formulated in terms of standard homological algebra and relies on the theory of Maurer-Cartan moduli and Maurer-Cartan twisting which is of independent interest.