IfG is a finitely generated group that is abelian or word-hyperbolic andH is an asynchronously combable group then every split extension ofG byH 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.
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Bridson, M.R. Combings of semidirect products and 3-manifold groups. Geometric and Functional Analysis 3, 263–278 (1993). https://doi.org/10.1007/BF01895689
1991 Mathematics Subject Classification