1. CMB 2016 (vol 59 pp. 244)
 Cao, Wensheng; Huang, Xiaolin

A Note on Quaternionic Hyperbolic Ideal Triangle Groups
In this paper, the quaternionic hyperbolic
ideal triangle groups are parameterized by a real oneparameter
family $\{\phi_s: s\in \mathbb{R}\}$. The indexing parameter $s$ is
the tangent of the quaternionic angular invariant of a triple
of points in $\partial \mathbf{H}_{\mathbb{h}}^2 $ forming this ideal
triangle. We show that if $s \gt \sqrt{125/3}$ then $\phi_s$ is
not a discrete embedding, and if $s \leq \sqrt{35}$
then $\phi_s$ is a discrete embedding.
Keywords:quaternionic inversion, ideal triangle group, quaternionic Cartan angular invariant Categories:20F67, 22E40, 30F40 

2. CMB 2015 (vol 59 pp. 170)
 MartínezPedroza, Eduardo

A Note on Fine Graphs and Homological Isoperimetric Inequalities
In the framework of homological characterizations of relative
hyperbolicity, Groves and Manning posed the question of whether
a simply connected $2$complex $X$ with a linear homological
isoperimetric inequality, a bound on the length of attaching
maps of $2$cells and finitely many $2$cells adjacent to any
edge must have a fine $1$skeleton. We provide a positive answer
to this question. We revisit a homological characterization
of relative hyperbolicity, and show that a group $G$ is hyperbolic
relative to a collection of subgroups $\mathcal P$ if and only if
$G$ acts cocompactly with finite edge stabilizers on an connected
$2$dimensional cell complex with a linear homological isoperimetric
inequality and $\mathcal P$ is a collection of representatives of
conjugacy classes of vertex stabilizers.
Keywords:isoperimetric functions, Dehn functions, hyperbolic groups Categories:20F67, 05C10, 20J05, 57M60 
