MilnorFaserung

MilnorFaserung is a theoretical concept in algebraic topology, primarily associated with the work of mathematician John Milnor. It refers to a specific type of fiber bundle construction where the fiber is a discrete set of points, and the total space is obtained by "twisting" these fibers over a base space. This twisting is governed by a map, often called a monodromy, which describes how the fibers are permuted as one moves around loops in the base space.

The term "Faserung" is German for "fiber bundle." Milnor's work explored how such twisted fiber bundles could be used to understand the topology of certain spaces, particularly those arising in algebraic geometry and differential geometry. A key aspect of MilnorFaserung is its connection to the concept of the Milnor fiber of an isolated singularity. When a complex analytic function has an isolated singularity at the origin, the intersection of its zero set with a small sphere centered at the origin often forms a sphere whose "neighborhood" can be viewed as a Milnor fiber bundle.

The topology of this Milnor fiber is intimately related to the local structure of the singularity. Studying the monodromy of this bundle provides crucial information about the singularity's invariants, such as its Milnor number. This approach has proven to be a powerful tool for classifying and understanding singularities. The study of MilnorFaserung has also found applications in areas like knot theory and the theory of algebraic curves.