Surfaces in the figure-8 knot complement. (English) Zbl 0924.57018

In the paper under review, the authors use the polyhedral structure of the figure eight knot complement to examine various normal surfaces in the manifold, give some technical conditions for such normal surfaces to be regular (without branch points) and a sufficient condition for such normal surfaces to be compressible in the manifold. The authors also give a criterion for a normal surfaces in a cubed 3-manifold, i.e. a 3-manifold admitting a cubing of non-positive curvature, to be incompressible.


57N10 Topology of general \(3\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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