On diffeomorphisms of even-dimensional discs

TL;DR

This paper computes the rational homotopy groups of the classifying space of diffeomorphisms of even-dimensional discs in a broad degree range, revealing a structured pattern beyond known stability ranges.

Contribution

It provides a complete calculation of these homotopy groups up to degree 4n-10 and uncovers a systematic structure outside specific degree bands, extending previous stability results.

Findings

Homotopy groups determined for degrees ≤ 4n-10

Discovery of systematic patterns outside certain degree bands

Extension beyond pseudoisotopy stable range

Abstract

We determine $\pi_*(BDiff_\partial(D^{2n})) \otimes \mathbb{Q}$ for $2n \geq 6$ completely in degrees $* \leq 4n-10$, 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.