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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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Additional Information

D. V. Osin
Affiliation: Department of Mathematics, City College of CUNY, New York, NY 10031
Email: denis.osin@gmail.com

DOI: https://doi.org/10.1090/S1079-6762-06-00159-4
Received by editor(s): November 7, 2005
Published electronically: April 28, 2006
Communicated by: Efim Zelmanov
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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