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Dehn filling in relatively hyperbolic groups

Groves, Daniel and Manning, Jason Fox (2008) Dehn filling in relatively hyperbolic groups. Israel Journal of Mathematics, 168 (1). pp. 317-429. ISSN 0021-2172. doi:10.1007/s11856-008-1070-6.

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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.

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Additional Information:Received September 14, 2006 and in revised form June 18, 2007. The first author [D.G] 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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National Science FoundationDMS-0504251
California Institute of Technology, Taussky-Todd FellowshipUNSPECIFIED
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Record Number:CaltechAUTHORS:GROijm08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12009
Deposited By: Archive Administrator
Deposited On:18 Oct 2008 03:53
Last Modified:08 Nov 2021 22:23

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