On diffeomorphisms of even-dimensional discs

Kupers, Alexander; Randal-Williams, Oscar

doi:10.1090/jams/1040

On diffeomorphisms of even-dimensional discs
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by Alexander Kupers and Oscar Randal-Williams;

J. Amer. Math. Soc.

DOI: https://doi.org/10.1090/jams/1040

Published electronically: January 18, 2024

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Abstract:

We determine $\pi _*(B\operatorname {Diff}_\partial (D^{2n})) \otimes \mathbb {Q}$ 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.

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