Abstract
In the late 1970’s, Thurston dramatically changed the nature of 3-manifold theory with the introduction of his Geometrisation Conjecture, and by proving it in the case of Haken 3-manifolds [23]. The conjecture for general closed orientable 3-manifolds remains perhaps the most important unsolved problem in the subject. A weaker form of the conjecture [19] deals with the fundamental group of a closed orientable 3-manifold. It proposes that either it contains Z ⊕ Z as a subgroup or it is word hyperbolic, in the sense of Gromov [11]. Word hyperbolic groups are precisely those groups which satisfy a linear isoperimetric inequality. They are of fundamental importance in geometric group theory and have very many useful properties.
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