# Lamination (topology)

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Lamination (topology)
Lamination associated with Mandelbrot set
Lamination of rabbit Julia set

In topology, a branch of mathematics, a lamination is a :

• "A topological space partitioned into subsets"[1]
• decoration (a structure or property at a point) of a manifold in which some subset of the manifold is partitioned into sheets of some lower dimension, and the sheets are locally parallel.

Lamination of surface is a partition of closed subset of surface into unions of smooth curves

It may or may not be possible to fill the gaps in a lamination to make a foliation.[2]

## Examples

• A geodesic lamination of a 2-dimensional hyperbolic manifold is a closed subset together with a foliation of this closed subset by geodesics[3]. 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.[4] These laminations are associated with quadratic maps [5][6]. It is a closed collection of chords in the unit disc [7]. It is also topological model of Mandelbrot or Julia set.