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- W3100696609 abstract "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. Various applications of these results are discussed." @default.
- W3100696609 created "2020-11-23" @default.
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- W3100696609 date "2006-10-03" @default.
- W3100696609 modified "2023-09-25" @default.
- W3100696609 title "Peripheral fillings of relatively hyperbolic groups" @default.
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- W3100696609 doi "https://doi.org/10.1007/s00222-006-0012-3" @default.
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