Weyl chamber length compactification of the PSL(2,R) x PSL(2,R) maximal character variety - Burger, Marc; Iozzi, Alessandra; Parreau, Anne; Pozzetti, Maria Beatrice (The Glasgow mathematical journal, 2025)
We study the vectorial length compactification of the space of conjugacy classes of maximal representations of the fundamental group ΓΓΓ of a closed hyperbolic surface ΣΣΣ in PSL(2,R)nPSL(2,R)nPSL(2,{\mathbb{R}})^n. We identify the boundary with the sphere P((ML)n)P((ML)n){\mathbb{P}}(({\mathcal{ML}})^n), where MLML\mathcal{ML} is the space of measured geodesic laminations on ΣΣΣ. In the case n=2n=2n=2, we give a geometric interpretation of the boundary as the space of homothety classes of R2R2{\mathbb{R}}^2-mixed structures on ΣΣΣ. We associate to such a structure a dual tree-graded space endowed with an R2+R2+{\mathbb{R}}_+^2-valued metric, which we show to be universal with respect to actions on products of two RR\mathbb{R}-trees with the given length spectrum.
Online veröffentlicht: 27. September 2024
Gesehen am 26.03.2025