In the mathematical field of knot theory, a2-bridge knot is aknot which can beregular isotoped so that the natural height function given by thez-coordinate has only two maxima and two minima as critical points. Equivalently, these are the knots with bridge number 2, the smallest possible bridge number for a nontrivial knot.
Other names for 2-bridge knots arerational knots,4-plats, andViergeflechte (German for 'four braids'). 2-bridge links are defined similarly as above, but each component will have one min and max. 2-bridge knots were classified by Horst Schubert, using the fact that the 2-sheeted branched cover of the 3-sphere over the knot is a lens space.
The namesrational knot andrational link were coined byJohn Conway who defined them as arising from numerator closures of rational tangles.This definition can be used to give a bijection between the set of 2-bridge links and the set of rational numbers; the rational number associated to a given link is calledtheSchubert normal form of the link (as this invariant was first defined by Schubert[1]), and is precisely the fraction associated to therational tangle whose numerator closure gives the link.[2]: chapter 10
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