Fillings, finite generation and direct limits of relatively hyperbolic groups (with J.F. Manning. Preprint (2006). .pdf

Abstract We examinine the relationship between finitely and infinitely generated relatively hyperbolic groups, in two different contexts. First, we elaborate on a remark from [1], which states that the version of Dehn filling in relatively hyperbolic groups proved by Osin in [13], allowing infinitely generated parabolic subgroups, follows from the version with finitely generated parabolics. Second, we observe that direct limits of relatively hyperbolic groups are in fact direct limits of finitely generated relatively hyperbolic groups. We use this (and known results) to derive some consequences about the Strong Novikov Conjecture for groups as constructed in [14].