Fibered knot

In knot theory, a branch of mathematics, a knot or link

is called fibered or fibred (sometimes Neuwirth knot in older texts, after Lee Neuwirth) if there is a 1-parameter family

runs through the points of the unit circle

For example: The Alexander polynomial of a fibered knot is monic, i.e. the coefficients of the highest and lowest powers of t are plus or minus 1.

Examples of knots with nonmonic Alexander polynomials abound, for example the twist knots have Alexander polynomials

[1] In particular the stevedore knot is not fibered.

Fibered knots and links arise naturally, but not exclusively, in complex algebraic geometry.

For instance, each singular point of a complex plane curve can be described topologically as the cone on a fibered knot or link called the link of the singularity.

The trefoil knot is the link of the cusp singularity

; the Hopf link (oriented correctly) is the link of the node singularity

In these cases, the family of Seifert surfaces is an aspect of the Milnor fibration of the singularity.

A knot is fibered if and only if it is the binding of some open book decomposition of