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About: Conway sphere     Goto   Sponge   NotDistinct   Permalink

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In mathematical knot theory, a Conway sphere, named after John Horton Conway, is a 2-sphere intersecting a given knot or link in a 3-manifold transversely in four points. In a knot diagram, a Conway sphere can be represented by a simple closed curve crossing four points of the knot, the cross-section of the sphere; such a curve does not always exist for an arbitrary knot diagram of a knot with a Conway sphere, but it is always possible to choose a diagram for the knot in which the sphere can be depicted in this way.A Conway sphere is essential if it is incompressible in the knot complement. Sometimes, this condition is included in the definition of Conway spheres.