In knot theory, a branch of mathematics, a knot or link in the 3dimensional sphere is called fibered or fibred (sometimes Neuwirth knot in older texts, after Lee Neuwirth) if there is a 1parameter family of Seifert surfaces for , where the parameter runs through the points of the unit circle , such that if is not equal to then the intersection of and is exactly .
For example:
 The unknot, trefoil knot, and figureeight 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 ; 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 .
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Trefoil knot
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Contents
Knots that are not fibered
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 − (2q + 1) + qt^{−1}, where q is the number of halftwists.^{[1]} In particular the Stevedore's knot is not fibered.
See also
References
 ^ "[dgga/9612014] Knots, Links, and 4Manifolds". Arxiv.org. Retrieved 20140419.
External links
 "How to construct all fibered knots and links". Topology. 21: 263–280. doi:10.1016/00409383(82)90009X.
 http://www.msp.warwick.ac.uk/gt/2010/1404/p050.xhtml