Algorithms for the complete decomposition of a closed \(3\)-manifold (Q1909529)

The authors refine the notion of normal surface introduced by \textit{W. Haken} [Acta Math. 105, 245-375 (1961; Zbl 0100.19402)]. The normal surface was utilized by Haken to produce a series of important algorithms (e.g., computing knot genus) for 3-dimensional manifolds. The refinement in question singles out ``vertex surfaces'' among the normal surfaces, and it is shown that these lead to simpler and more efficient algorithms than those previously known.