An algorithm to decide if a 3-manifold is a Haken manifold
The authors develop an algorithm which determines whether a closed, irreducible 3-manifold M (given by a handle-decomposition) contains an injective surface \(F\neq S^ 2\) (i.e. \(\pi_ 1(F)\to \pi_ 1(M)\) is injective). In fact, if there are any injective surfaces in M this algorithm will actually produce one. An essential ingredient of the proof is \textit{W. Haken}'s classical theory of normal surfaces [Acta Math. 105, 245-375 (1961; Zbl 0100.194)].
scientific article; zbMATH DE number 3868241