In knot theory, a branch of mathematics, a knot or link
K
in the 3-dimensional sphere
S
3
is called **fibered** or **fibred** (sometimes **Neuwirth knot** in older texts, after Lee Neuwirth) if there is a 1-parameter family
F
t
of Seifert surfaces for
K
, where the parameter
t
runs through the points of the unit circle
S
1
, such that if
s
is not equal to
t
then the intersection of
F
s
and
F
t
is exactly
K
.

For example:

The unknot, trefoil knot, and figure-eight knot are fibered knots.
The Hopf link is a fibered link.
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
z
2
+
w
3
; the Hopf link (oriented correctly) is the link of the node singularity
z
2
+
w
2
. 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
S
3
.

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 *qt* − (2*q* + 1) + *qt*^{−1}, where *q* is the number of half-twists. In particular the Stevedore's knot is not fibered.