Dehn filling in relatively hyperbolic groups |
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Authors: | Daniel Groves Jason Fox Manning |
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Institution: | (1) California Institute of Technology, California, USA;(2) University at Buffalo, SUNY, Buffalo, USA |
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Abstract: | 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 2π Theorem in the context of relatively hyperbolic
groups.
The first author was supported in part by NSF Grant DMS-0504251.
The second author was supported in part by an NSF Mathematical Sciences Post-doctoral Research Fellowship.
Both authors thank the NSF for their support. Most of this work was done while both authors were Taussky-Todd Fellows at Caltech. |
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