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 define a new condition on relatively hyperbolic Dehn filling which allows us to control the
behavior of a relatively quasiconvex subgroups which need not be full. As an application, in …

This is the first paper of three papers in a row aiming to study cohomology of group theoretic
Dehn fillings. In the present paper, we prove a particular free product structure, which is …

We define a new condition on relatively hyperbolic Dehn filling which allows us to control the
behavior of a relatively quasiconvex subgroups which need not be full. As an application, in …

Given a hyperbolic group $ G $ and a maximal infinite cyclic subgroup $\langle g\rangle $,
we define a drilling of $ G $ along $ g $, which is a relatively hyperbolic group pair …

We show that the existence of a nonparabolic local cut point in the Bowditch boundary∂(G,
ℙ) of a relatively hyperbolic group (G, ℙ) implies that G splits over a 2–ended subgroup. This …

In this paper we provide a classification theorem for one‐dimensional boundaries of groups
with isolated flats. Given a group Γ acting geometrically on a CAT (0) space X with isolated …

We prove that for $ n\geq 2$, a non-uniform lattice in $\text {PU}(n, 1) $ does not admit a
relatively geometric action on a $\mathrm {CAT}(0) $ cube complex, in the sense of Einstein …

In this article, we prove a version of Martin and Skora's conjecture that convergence groups
on the $2 $-sphere are covered by Kleinian groups. Given a relatively hyperbolic group pair …

We establish that standard arithmetic subgroups of a special orthogonal group SO (1, n) are
conjugacy separable. As an application we deduce this property for unit groups of certain …