On a volume element of a Hitchin component
On a volume element of a Hitchin component
Let $\varSigma$ be a closed oriented Riemann surface of genus at least $2$. By using symplectic chain complex, we construct a volume element for a Hitchin component of $\mathrm{Hom}(\pi_1(\varSigma),\mathrm{PSL}_n(\mathbb{R}))/\mathrm{PSL}_n(\mathbb