The \({\textit{SU}}(2)\)-character variety of the closed surface of genus 2

We study the symplectic geometry of the \({\text {SU}}(2)\)-representation variety of the compact oriented surface of genus 2. We use the Goldman flows to identify subsets of the moduli space with corresponding subsets of \({\mathbb {P}}^3(\mathbb {C})\). We also define and study two antisymplectic involutions on the moduli space and their fixed point sets.