Peripheral fillings of relatively hyperbolic groups

Osin, D.¹

¹Department of Mathematics, City College of CUNY, New York, NY 10031

Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 44-52

Résumé

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.

Détail

DOI : 10.1090/S1079-6762-06-00159-4

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