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Peripheral fillings of relatively hyperbolic groups

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, The City College of New York, New York, NY, 138th street and Convent Ave., 10031, USA

    Denis V. Osin

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  1. Denis V. Osin
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Correspondence to Denis V. Osin.

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Mathematics Subject Classification (2000)

20F65, 20F67, 20F06, 57M27, 20E26

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Osin, D. Peripheral fillings of relatively hyperbolic groups. Invent. math. 167, 295–326 (2007). https://doi.org/10.1007/s00222-006-0012-3

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  • DOI: https://doi.org/10.1007/s00222-006-0012-3

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