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

Suppose that a compact quantum group Q acts faithfully on a smooth, compact, connected manifold M, i.e. has a C* (co)-action alpha on C(M), such that alpha(C-infinity(M)) subset of C-infinity (M, Q) and the linear span of alpha(C-infinity(M))(1 circle times Q) is dense in C-infinity(M, Q) with respect to the Frechet topology. It was conjectured by the author quite a few years ago that Q must be commutative as a C* algebra i.e. Q congruent to 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. (C) 2020 Elsevier Inc. All rights reserved.