L∞ rational homotopy of mapping spaces

In this paper we describe explicit L∞ algebras modeling the rational homotopy type of any component of the spaces map(X, Y ) and map*(X, Y ) of free and pointed maps between the finite nilpotent CW-complex X and the finite type nilpotent CW-complex Y When X is of finite type, non necessarily finite, we also show that the algebraic covers of these L∞ algebras model the universal covers of the corresponding mapping spaces. © 2012 Universidad Complutense de Madrid