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- Title
Peripheral fillings of relatively hyperbolic groups.
- Authors
Osin, Denis V.
- Abstract
In this paper a group theoretic version of Dehn surgery is studied. Starting with an arbitrary relatively hyperbolic group G we define a peripheral filling procedure, which produces quotients of G by imitating the effect of the Dehn filling of a complete finite volume hyperbolic 3-manifold M on the fundamental group π1( M). The main result of the paper is an algebraic counterpart of Thurston’s hyperbolic Dehn surgery theorem. We also show that peripheral subgroups of G ‘almost’ have the Congruence Extension Property and the group G is approximated (in an algebraic sense) by its quotients obtained by peripheral fillings.
- Subjects
DEHN surgery (Topology); HYPERBOLIC groups; GROUP theory; SURGERY (Topology); ALGEBRA; MATHEMATICS
- Publication
Inventiones Mathematicae, 2007, Vol 167, Issue 2, p295
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-006-0012-3