A differential topology proof that the $SU(2)$ character variety of the genus two surface is homeomorphic to $\mathbb{C}{P}^3$

Christopher M. Herald, Paul Kirk

We provide a proof that the $SU(2)$ character variety of a genus two surface, $\ddot{I}‡(F_2)$, is a closed compact manifold, and a proof of the Narasimhan-Ramanan theorem that $\ddot{I}‡(F_2)$…