Peripheral fillings of relatively hyperbolic groups
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 . 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. Various applications of these results are discussed.
Cite
@article{arxiv.math/0510195,
title = {Peripheral fillings of relatively hyperbolic groups},
author = {D. Osin},
journal= {arXiv preprint arXiv:math/0510195},
year = {2009}
}
Comments
The difference with the previous version is that Proposition 3.2 is proved for quasi--geodesics instead of geodesics. This allows to simplify the exposition in the last section. To appear in Invent. Math