Remote Access Electronic Research Announcements

Electronic Research Announcements

ISSN 1079-6762



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
Published electronically: April 28, 2006
MathSciNet review: 2218630
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Electronic Research Announcements of the American Mathematical Society with MSC (2000): 20F65, 20F67, 57M27

Retrieve articles in all journals with MSC (2000): 20F65, 20F67, 57M27

Additional Information

D. V. Osin
Affiliation: Department of Mathematics, City College of CUNY, New York, NY 10031

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.