Lamination (topology)

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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.

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]

Examples[edit]

Geodesic lamination of a closed surface

See also[edit]

Notes[edit]

  1. ^ Hazewinkel, Michiel, ed. (2001) [1994], "Lamination", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
  2. ^ "Archived copy". Archived from the original on 2009-07-13. Retrieved 2009-07-13. Oak Ridge National Laboratory
  3. ^ 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
  4. ^ 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
  5. ^ Tomoki KAWAHIRA: Topology of Lyubich-Minsky's laminations for quadratic maps: deformation and rigidity (3 heures)
  6. ^ Topological models for some quadratic rational maps by Vladlen Timorin
  7. ^ Modeling Julia Sets with Laminations: An Alternative Definition by Debra Mimbs Archived 2011-07-07 at the Wayback Machine.

References[edit]