Lamination (topology)

• "topological space partitioned into subsets"
• decoration of a manifold in which some subset of the manifold is partitioned into sheets of some lower dimension, and the sheets are locally parallel.

Examples

• A geodesic lamination of a 2-dimensional hyperbolic manifold is a closed subset together with a foliation of this closed subset by geodesics. These are used in Thurston's classification of elements of the mapping class group and in his theory of earthquake maps.
• Quadratic laminations, which remain invariant under the angle doubling map. These laminations are associated with quadratic maps. It is a closed collection of chords in the unit disc. It is also topological model of Mandelbrot or Julia set.