On diffeomorphisms of even-dimensional discs

We determine ${\pi }_{\ast }(BDif{f}_{\mathrm{\partial }}(D^{2n}))\otimes \mathbb{Q}$ for $2n \geq 6$completelyindegrees$* \leq 4n-10$, far beyond the pseudoisotopy stable range. Furthermore, above these degrees we discover a systematic structure in these homotopy groups: we determine them outside of certain “bands” of degrees.