Bounded cohomology of diffeomorphism groups of higher dimensional spheres

Abstract

In this paper we prove the vanishing of the bounded cohomology of ${\text{Diff}}_{+}^r(S^n)$ with real coefficients when $n\ge 4$ and $1\le r\le \infty$. This answers the question raised in \cite{FNS24} for $\ge 4$ dimensional spheres.

Comments are welcomed!