Peripheral fillings of relatively hyperbolic groups

Osin, D.

doi:10.1090/S1079-6762-06-00159-4

Peripheral fillings of relatively hyperbolic groups

Author: D. V. Osin
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 44-52
MSC (2000): Primary 20F65, 20F67, 57M27
DOI: https://doi.org/10.1090/S1079-6762-06-00159-4
Published electronically: April 28, 2006
MathSciNet review: 2218630
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Abstract: 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 $\pi _1(M)$. The main result of the paper is an algebraic counterpart of Thurston’s hyperbolic Dehn surgery theorem. We also show that peripheral subgroups of $G$ “almost” have the Congruence Extension Property and the group $G$ is approximated (in an algebraic sense) by its quotients obtained by peripheral fillings.

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