Fillings, finite generation and direct limits of relatively hyperbolic groups

Details Fillings, finite generation and direct limits of relatively hyperbolic groups Fillings, finite generation and direct limits of relatively hyperbolic groups

2006-06-02

arxiv.org/abs/math/0606070v2

Mathematics

Group Theory

(v1)10 pages. (v2) 11 pages, to appear in Groups, Geometry and Dynamics

Scientific paper

We examine the relationship between finitely and infinitely generated relatively hyperbolic groups, in two different contexts. First, we elaborate on a remark from math.GR/0601311, which states that the version of Dehn filling in relatively hyperbolic groups proved in math.GR/0510195, 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 math.GR/0411039.

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