Peripheral fillings of relatively hyperbolic groups

Details Peripheral fillings of relatively hyperbolic groups Peripheral fillings of relatively hyperbolic groups

2005-10-10

arxiv.org/abs/math/0510195v3

Mathematics

Group Theory

The difference with the previous version is that Proposition 3.2 is proved for quasi--geodesics instead of geodesics. This all

Scientific paper

10.1007/s00222-006-0012-3

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.

Affiliated with

Also associated with

No associations

Rating

Peripheral fillings of relatively hyperbolic groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Peripheral fillings of relatively hyperbolic groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Peripheral fillings of relatively hyperbolic groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-505918