Peripheral fillings of relatively hyperbolic groups

被引：0
作者：
Denis V. Osin
机构：
[1] The City College of New York,Department of Mathematics
来源：
Inventiones mathematicae | 2007年 / 167卷
关键词：
Fundamental Group; Boundary Component; Cayley Graph; Osin; Hyperbolic Group;
D O I：
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摘要：
In this paper 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 π1(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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页码：295 / 326
页数：31
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