Montesinos link

A Montesinos link. In this example, e=-3 , \alpha_1 /\beta_1=-3/2 and \alpha_2 /\beta_2=5/2 .

In the mathematical theory of knots, a Montesinos link is a special kind of link that generalizes pretzel links. A Montesinos link which is also a knot (i.e. a link with one component) is a Montesinos knot.

Notation

A Montesinos link is composed of several rational tangles. One notation for a Montesinos link is K(e;\alpha_1 /\beta_1,\alpha_2  /\beta_2,\ldots,\alpha_n  /\beta_n).[1]

In this notation, e and all the \alpha_i and \beta_i are integers. The Montesinos link given by this notation consists of the sum of the rational tangles given by the integer e and the rational tangles \alpha_1 /\beta_1,\alpha_2  /\beta_2,\ldots,\alpha_n  /\beta_n

A pretzel link can also be described as a Montesinos link with integer tangles.

References

  1. Zieschang, Heiner. "Classification of Montesinos knots." Topology. Springer Berlin Heidelberg, 1984. 378–389

Further reading

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