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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.06106
 Bibcode:
 2021arXiv211006106M
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Metric Geometry
 EPrint:
 25 pages