Peripheral fillings of relatively hyperbolic groups

• 成果类型: Article
• 署名作者: Osin, Denis V.
• 署名单位: City University of New York (CUNY) System; City College of New York (CUNY)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-006-0012-3
• 发表日期: 2007
• 页码: 295-326
• 关键词: spaces

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 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.