Andrey Lazarev (University of Bristol)
A.Lazarev@bristol.ac.uk
Let X and Y be two rational spaces, both nilpotent and of finite type and F :X → Y a fixed map. We are interested in rational homotopy groups of the mapping space F(X,Y) where f is taken to be a basepoint. The result is formulated in terms of the de Rham-Sullivan algebras of X and Y. In the case X=Y and X a finite CW-complex or a finite Postnikov tower we can say more. It is known that the homotopy classes of self-homotopy equivalences of X is a group of rational points of an algebraic group over Q. We identify its Lie algebra as the zeroth Harrison cohomology of the Sullivan-de Rham algebra of X with the Gerstenhaber bracket.