Convex co-compact groups with one-dimensional boundary faces (Q6619324)

In the paper under review, the authors consider the class of (naive) convex co-compact subgroups of \(\mathrm{PGL}_{d}(\mathbb{R})\) as defined in [\textit{J. Danciger} et al., Geom. Dedicata 192, 87--126 (2018; Zbl 1428.53078)]. In [Geom. Topol. 27, No. 2, 417--511 (2023; Zbl 1515.20241)], the authors proved a general, geometric characterization of when such a group is relatively hyperbolic with respect to a (possibly empty) collection of virtually abelian subgroups of rank at least \(2\).\N\NIn this paper, they specialize to the case of virtually abelian subgroups of rank exactly \(2\) and provide a very simple characterization in terms of the ideal boundary of the associated convex hull.