A closed ball compactification of a maximal component via cores of trees

Abstract

We show that, in the character variety of surface group representations into the Lie group $\mathrm{PSL}(2,\mathbb{R})\times \mathrm{PSL}(2,\mathbb{R})$, the compactification of the maximal component introduced by the second author is a closed ball upon which the mapping class group acts. We study the dynamics of this action. Finally, we describe the boundary points geometrically as $(\overline{A_1\times A_1},2)$-valued mixed structures.

arXiv comment25 pages