## The spin-statistics theorem and the Berry-Robbins problem

In 1 , Berry and Robbins propose an interesting way to obtain the spin-statistics theorem, which is close to the famous belt trick, though expressed more mathematically. They completely explain their construction for $2$ particles, but while attempting to extend their construction to $n$ particles, they faced a technical obstruction. This led to the Berry-Robbins problem. Let $C_n(\mathbb{R}^3)$ denote the configuration space of $n$ distinct particles. Then the symmetric group $S_n$ acts on $C_n(\mathbb{R}^3)$ by permuting the components of any…