An algorithm to decide if a 3-manifold is a Haken manifold. (English) Zbl 0545.57003

Jaco, William; Oertel, Ulrich

Topology 23, 195-209 (1984).

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 W. Haken’s classical theory of normal surfaces [Acta Math. 105, 245-375 (1961; Zbl 0100.194)].

Reviewer: D.Repovš

MSC:

57N10	Topology of general \(3\)-manifolds (MSC2010)
57M35	Dehn’s lemma, sphere theorem, loop theorem, asphericity (MSC2010)
57M05	Fundamental group, presentations, free differential calculus

Keywords:

incompressible surface; irreducible 3-manifold; handle-decomposition; injective surfaces; algorithm; normal surfaces

Citations:

Zbl 0100.194