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. https://resolver.caltech.edu/CaltechAUTHORS:GROijm08
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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.
Item Type: | Article | ||||||
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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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Issue or Number: | 1 | ||||||
DOI: | 10.1007/s11856-008-1070-6 | ||||||
Record Number: | CaltechAUTHORS:GROijm08 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:GROijm08 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 12009 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Archive Administrator | ||||||
Deposited On: | 18 Oct 2008 03:53 | ||||||
Last Modified: | 08 Nov 2021 22:23 |
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