Weyl chamber length compactification of the ${\rm PSL}(2,\mathbb
R)\times{\rm PSL}(2,\mathbb R)$ maximal character variety
Weyl chamber length compactification of the ${\rm PSL}(2,\mathbb
R)\times{\rm PSL}(2,\mathbb R)$ maximal character variety
We study the vectorial length compactification of the space of conjugacy classes of maximal representations of the fundamental group $\Gamma$ of a closed hyperbolic surface $\Sigma$ in ${\rm PSL}(2,\mathbb R)^n$. We identify the boundary with the sphere $\mathbb P((\mathcal{ML})^n)$, where $\mathcal{ML}$ is the space of measured geodesic laminations on $\Sigma$. …