Lamination (topology) explained

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

"topological space partitioned into subsets"
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.^[1]

Examples

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

Web site: Defs.txt . 2009-07-13 . dead . https://web.archive.org/web/20090713073050/http://www.ornl.gov/sci/ortep/topology/defs.txt . 2009-07-13 . Oak Ridge National Laboratory
https://www.ams.org/bookstore-getitem/item=CONM-269 Laminations and foliations in dynamics, geometry and topology: proceedings of the conference on laminations and foliations in dynamics, geometry and topology, May 18-24, 1998, SUNY at Stony Brook
http://www.allacademic.com/meta/p_mla_apa_research_citation/4/3/5/9/2/p435923_index.html Houghton, Jeffrey. "Useful Tools in the Study of Laminations" Paper presented at the annual meeting of the Mathematical Association of America MathFest, Omni William Penn, Pittsburgh, PA, Aug 05, 2010
http://people.math.jussieu.fr/~favre/Dyn-comp.html Tomoki KAWAHIRA: Topology of Lyubich-Minsky's laminations for quadratic maps: deformation and rigidity (3 heures)
http://www.mccme.ru/~timorin/publ/QuadRat.pdf Topological models for some quadratic rational maps by Vladlen Timorin
http://atlas-conferences.com/cgi-bin/abstract/cbaj-28 Modeling Julia Sets with Laminations: An Alternative Definition by Debra Mimbs