Abstract We compute the rational homotopy groups in degrees up to approximately 32d 3 2 d of the group of diffeomorphisms of a closed d d -dimensional disc fixing the boundary. Based on this we determine the optimal rational concordance stable range for high-dimensional discs, describe the rational homotopy type of B Top (d) B Top (d) in a range, and calculate the second rational derivative of the functor B Top (-) B Top (−) in the sense of Weiss’ orthogonal calculus.
Krannich et al. (Fri,) studied this question.