Anosov representations give a higher-rank analogue of convex cocompactness in a rank-
one Lie group which shares many of its good geometric and dynamical properties; …

The 'contracting boundary'of a proper geodesic metric space consists of equivalence
classes of geodesic rays that behave like rays in a hyperbolic space. We introduce a …

We begin an investigation into the behavior of Bowditch and Gromov boundaries under the
operation of Dehn filling. In particular, we show many Dehn fillings of a toral relatively …

We prove that divergent, extended geometrically finite (in the sense of Weisman arXiv:
2205.07183) representations can be interpreted as restricted Anosov (in the sense of …

In this paper we provide a procedure to obtain a non-trivial HHS structure on a hyperbolic
space. In particular, we prove that given a finite collection $\mathcal {F} $ of quasi-convex …

We introduce and study\emph {simple Anosov representations} of closed hyperbolic surface
groups, analogous to Minsky's\emph {primitive stable representations} of free groups. We …

We present an algorithm that computes Bowditch's canonical JSJ decomposition of a given
one‐ended hyperbolic group over its virtually cyclic subgroups. The algorithm works by …

We show that under appropriate assumptions, a blown-up corona of a relatively hyperbolic
group is equivariant and the compactification of the universal space for proper action by the …

We prove that the fundamental group of a finite graph of convergence groups with parabolic
edge groups is a convergence group. Using this result, under some mild assumptions, we …

We show that except for one exceptional case, a lamination on the boundary of a 3-
dimensional handlebody H is a Hausdorff limit of meridians if and only if it is commensurable …