Combings of semidirect products and 3-manifold groups

If G is a finitely generated group that is abelian or word-hyperbolic and H is an asynchronously combable group then every split extension of G by H is asynchronously combable. The fundamental group of any compact 3-manifold that satisfies the geometrization conjecture is asynchronously combable. Every split extension of a word-hyperbolic group by an asynchronously automatic group is asynchronously automatic. © 1993 Birkhäuser Verlag.