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Lamination (topology)
In topology, a branch of mathematics, a lamination is a :
* "A topological space partitioned into subsets"〔(Lamination in The Online Encyclopaedia of Mathematics 2002 Springer-Verlag Berlin Heidelberg New York )〕
* 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.〔http://www.ornl.gov/sci/ortep/topology/defs.txt Oak Ridge National Laboratory〕
==Examples==
*A geodesic lamination of a 2-dimensional hyperbolic manifold is a closed subset together with a foliation of this closed subset by geodesics.〔(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 )〕 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.〔(Houghton, Jeffrey. "Useful Tools in the Study of Laminations" Paper presented at the annual meeting of the The Mathematical Association of America MathFest, Omni William Penn, Pittsburgh, PA, Aug 05, 2010 )〕 These laminations are associated with quadratic maps.〔(Tomoki KAWAHIRA: Topology of Lyubich-Minsky's laminations for quadratic maps: deformation and rigidity (3 heures) )〕〔(Topological models for some quadratic rational maps by Vladlen Timorin )〕 It is a closed collection of chords in the unit disc.〔(Modeling Julia Sets with Laminations: An Alternative Definition by Debra Mimbs )〕 It is also topological model of Mandelbrot or Julia set.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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