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Description

Just as Gromov hyperbolic groups are a coarse geometric generalization of cocompact Kleinian groups (fundamental groups of compact hyperbolic orbifolds), relatively hyperbolic groups are a coarse geometric generalization of Kleinian groups with finite covolume (fundamental groups of finite volume hyperbolic orbifolds). One consequence of the Dehn surgery theorem of Thurston is that most quotients of a hyperbolic knot complement group by the normal closure of a peripheral element are Gromov hyperbolic. We extend this result to groups which are hyperbolic relative to a finite collection of rank two free abelian groups. This is joint work with Daniel Groves.