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

Abstract

Suppose that a compact quantum group Q acts faithfully on a smooth, compact, connected manifold M , i.e. has a C * (co)-actionwith respect to the Fréchet topology. It was conjectured by the author quite a few years ago that Q must be commutative as a C * algebra i.e. Q ∼ = 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.