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ISSN 1079-6762

Peripheral fillings of relatively hyperbolic groups

Author(s): D. V. Osin
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 44-52.
MSC (2000): Primary 20F65, 20F67, 57M27
Posted: April 28, 2006
MathSciNet review: 2218630
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Abstract | References | Similar articles | Additional information

Abstract: A group-theoretic version of Dehn surgery is studied. Starting with an arbitrary relatively hyperbolic group we define a peripheral filling procedure, which produces quotients of by imitating the effect of the Dehn filling of a complete finite-volume hyperbolic 3-manifold on the fundamental group $\pi_1(M)$ . The main result of the paper is an algebraic counterpart of Thurston's hyperbolic Dehn surgery theorem. We also show that peripheral subgroups of ``almost'' have the Congruence Extension Property and the group is approximated (in an algebraic sense) by its quotients obtained by peripheral fillings.

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