Diffeomorphisms of discs and the second Weiss derivative of BTop(-)

Abstract

We compute the rational homotopy groups in degrees up to approximately $\frac{3}{2}$d of the group of diffeomorphisms of a closed 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 BTop(d) in a range, and calculate the second rational derivative of the functor BTop(-) in the sense of Weiss' orthogonal calculus.

84 pages, to appear in Inventiones Mathematicae