On diffeomorphisms of even-dimensional discs

Abstract

We determine π ∗ ( B Diff ∂ ⁡ ( D 2 n ) ) ⊗ Q \pi _*(B\operatorname {Diff}_\partial (D^{2n})) \otimes \mathbb {Q} for 2 n ≥ 6 2n \geq 6 completely in degrees ∗ ≤ 4 n − 10 * \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.