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Fibered Knot




in the 3-dimensional Sphere S^3 is called fibered (sometimes spelled '''fibred''') in case 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:



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.