# Word hyperbolic Dehn surgery

Lackenby, M

May 2000

## Journal:

INVENTIONES MATHEMATICAE

## Last Updated:

2019-09-09T18:42:51.557+01:00

2

140

243-282

## abstract:

The aim of this paper is to demonstrate that very many Dehn fillings on a
cusped hyperbolic 3-manifold yield a 3-manifold which is irreducible, atoroidal
and not Seifert fibred, and which has infinite, word hyperbolic fundamental
group. We establish an extension of the Thurston-Gromov $2\pi$ theorem by
showing that if each filling slope has length more than six, then the resulting
3-manifold has all the above properties. We also give a combinatorial version
of the $2\pi$ theorem which relates to angled ideal triangulations. We apply
these techniques by studying surgery along alternating links.

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