On a volume element of a Hitchin component
Volume 217 / 2012
Fundamenta Mathematicae 217 (2012), 249-264
MSC: Primary 57Q10, 53D30; Secondary 32G15.
DOI: 10.4064/fm217-3-4
Abstract
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 $\mathrm{Hom}(\pi_1(\varSigma),\mathrm{PSL}_n(\mathbb{R}))/\mathrm{PSL}_n(\mathbb{R})$ for $n > 2$.
