Non-existence of genuine (compact) quantum symmetries of compact, connected smooth manifolds

Suppose that a compact quantum group $\mathcal{Q}$ acts faithfully on a smooth, compact, connected manifold $M$, i.e. has a $C^{\ast }$ (co)-action $\alpha$ on $C(M)$, such that $\alpha(C^\infty(M)) \subseteq C^\infty(M, {\mathcal Q})$andthelinearspanof$\alpha(C^\infty(M))(1 \otimes {\mathcal Q})$isdensein$C^\infty(M, {\mathcal Q})$ with respect to the Frechet topology. It was conjectured by the author quite a few years ago that $\mathcal{Q}$ must be commutative as a $C^{\ast }$ algebra i.e. $\mathcal{Q}\cong C(G)$ for some compact group $G$ acting smoothly on $M$. The goal of this paper is to prove the truth of this conjecture. A remarkable aspect of the proof is the use of probabilistic techniques involving Brownian stopping time.