96 research outputs found
Peripheral fillings of relatively hyperbolic groups
A group theoretic version of Dehn surgery is studied. Starting with an
arbitrary relatively hyperbolic group we define a peripheral filling
procedure, which produces quotients of by imitating the effect of the Dehn
filling of a complete finite volume hyperbolic 3--manifold on the
fundamental group . The main result of the paper is an algebraic
counterpart of Thurston's hyperbolic Dehn surgery theorem. We also show that
peripheral subgroups of 'almost' have the Congruence Extension Property and
the group is approximated (in an algebraic sense) by its quotients obtained
by peripheral fillings. Various applications of these results are discussed.Comment: The difference with the previous version is that Proposition 3.2 is
proved for quasi--geodesics instead of geodesics. This allows to simplify the
exposition in the last section. To appear in Invent. Mat
On commensurable hyperbolic Coxeter groups
For Coxeter groups acting non-cocompactly but with finite covolume on real hyperbolic space Hn, new methods are presented to distinguish them up to (wide) commensurability. We exploit these ideas and determine the commensurability classes of all hyperbolic Coxeter groups whose fundamental polyhedra are pyramids over a product of two simplices of positive dimensions
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