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 .
YouTube Encyclopedic

1/3Views:1 9922 719346

✪ Trefoil knot

✪ David Morrison: Calabi–Yau manifolds, Mirror Symmetry, and Ftheory  Part I

✪ Convex Surfaces and Classification of Contact Structures (Ko Honda @ MSRI)
Transcription
Contents
Examples
Knots that are fibered
For example:
 The unknot, trefoil knot, and figureeight knot are fibered knots.
 The Hopf link is a fibered link.
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 , where q is the number of halftwists.^{[1]} In particular the stevedore knot is not fibered.
Related constructions
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 .
See also
References
 ^ Fintushel, Ronald; Stern, Ronald J. (1998). "Knots, Links, and 4Manifolds". Inventiones Mathematicae. 134 (2): 363–400. arXiv:dgga/9612014. doi:10.1007/s002220050268. MR 1650308.
External links
 Harer, John (1982). "How to construct all fibered knots and links". Topology. 21 (3): 263–280. doi:10.1016/00409383(82)90009X. MR 0649758.
 Gompf, Robert E.; Scharlemann, Martin; Thompson, Abigail (2010). "Fibered knots and potential counterexamples to the property 2R and sliceribbon conjectures". Geometry & Topology. 14 (4): 2305–2347. doi:10.2140/gt.2010.14.2305. MR 2740649.