Dehn filling in relatively hyperbolic groups

Details Dehn filling in relatively hyperbolic groups Dehn filling in relatively hyperbolic groups

2006-01-13

arxiv.org/abs/math/0601311v4

Israel Journal of Mathematics 168 (2008) 317--429

Mathematics

Group Theory

83 pages. v2: An improved version of preferred paths is given, in which preferred triangles no longer need feet. v3: Fixed sev

Scientific paper

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, "preferred paths", is combinatorial in nature and allows us to define the second, a relatively hyperbolic version of a construction of Mineyev. As an application, we prove a group-theoretic analog of the Gromov-Thurston 2\pi Theorem in the context of relatively hyperbolic groups.

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