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Relatively hyperbolic groups
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Bowditch, B. H. (2012) Relatively hyperbolic groups. International Journal of Algebra and Computation, Vol.22 (No.3). p. 1250016. doi:10.1142/S0218196712500166 ISSN 0218-1967.
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Official URL: http://dx.doi.org/10.1142/S0218196712500166
Abstract
In this paper we develop some of the foundations of the theory of relatively hyperbolic groups as originally formulated by Gromov. We prove the equivalence of two definitions of this notion. One is essentially that of a group admitting a properly discontinuous geometrically finite action on a proper hyperbolic space, that is, such that every limit point is either a conical limit point or a bounded parabolic point. The other is that of a group which admits a cofinite action on a connected fine hyperbolic graph. We define a graph to be "fine" if there are only finitely many circuits a given length containing any given edge, and we develop some of the properties of this notion. We show how a relatively hyperbolic group can be assumed to act on a proper hyperbolic space of a particular geometric form. We define the boundary of a relatively hyperbolic group, and show that the limit set of any geometrically finite action of the group is equivariantly homeomorphic to this boundary. This generalizes a result of Tukia for geometrically finite kleinian groups. We also describe when the boundary is connected. © 2012 World Scientific Publishing Company
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | International Journal of Algebra and Computation | ||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
ISSN: | 0218-1967 | ||||
Official Date: | May 2012 | ||||
Dates: |
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Volume: | Vol.22 | ||||
Number: | No.3 | ||||
Page Range: | p. 1250016 | ||||
DOI: | 10.1142/S0218196712500166 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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