Lamination (topology)

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

A lamination of a surface is a partition of a closed subset of the surface into smooth curves.

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

• 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.

• Train track (mathematics)
• Orbit portrait

• Conformal Laminations Thesis by Vineet Gupta, California Institute of Technology Pasadena, California 2004

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