Abstract We give technical conditions for a quasi-isometry of pairs to preserve subgroup being hyperbolically embedded. consider applications the and commensurability invariance acylindrical hyperbolicity finitely generated groups.

ABSTRACT This comment responds to Fabio Anderaos de Araujo’s article “Sraffa and the Labour Theory of Value: a note” (Araujo 2019), specifically addresses issue commensurability originally developed in Jefferies (2015).

We describe a general procedure to produce fundamental domains for complex hyperbolic triangle groups. This allows us new nonarithmetic lattices, bringing the number of known commensurability classes in PU(2,1) 22.

The purpose of this note is to present a criterion for an infinite collection of distinct hyperbolic 3-manifolds to be commensurably infinite. (Here, a collection of hyperbolic 3-manifolds is commensurably infinite if it contains representatives from infinitely many commensurability classes.) Namely, such a collection M is commensurably infinite if there is a uniform upper bound on the volumes ...