An algorithm to decide if a 3-manifold is a Haken manifold (Q797188)
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scientific article; zbMATH DE number 3868241
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An algorithm to decide if a 3-manifold is a Haken manifold |
scientific article; zbMATH DE number 3868241 |
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An algorithm to decide if a 3-manifold is a Haken manifold (English)
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1984
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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)].
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incompressible surface
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irreducible 3-manifold
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handle-decomposition
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injective surfaces
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algorithm
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normal surfaces
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