On diffeomorphisms of even-dimensional discs

Abstract

We determine ${\pi }_{\ast }(BDif{f}_{\partial }(D^{2n}))\otimes \mathbb{Q}$ for $2n\ge 6$ completely in degrees $\ast \le 4n-10$, 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.

99 pages, to appear in Journal of the AMS