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2-bridge knot

In mathematics, a 2-bridge knot is a knot which can be isotoped so that the natural height function given by the z-coordinate has only two maxima and two minima as critical points.

Other names for 2-bridge knots are rational knots, 4-plats, and Viergeflechte. 2-bridge links are defined similarly as above, but each component will have one min and max. 2-bridge knots were classified by Seifert, using the fact that the 2-sheeted branched cover of the 3-sphere over the knot is a lens space.

The names rational knot and rational link were coined by John Conway who defined them as arising from numerator closures of rational tangles.

See also

• bridge number

External links

• Table and invariants of rational knots with up to 16 crossings