Peripheral fillings of relatively hyperbolic groups |
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Authors: | Denis V Osin |
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Institution: | (1) Department of Mathematics, The City College of New York, New York, NY 138th street and Convent Ave., 10031, USA |
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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.
Mathematics Subject Classification (2000) 20F65, 20F67, 20F06, 57M27, 20E26 |
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