Measured laminations in 3-manifolds

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Abstract

An essential measured lamination embedded in an irreducible, orientable 3-manifold M is a codimension 1 lamination with a transverse measure, carried by an incompressible branched surface satisfying further technical conditions. Weighted incompressible surfaces are examples of essential measured laminations, and the inclusion of a leaf of an essential measured lamination into M is injective on 7ri. There is a space P£(M) whose points are projective classes of essential measured laminations. Projective classes of weighted incompressible surfaces are dense in P£(M). The space P£(M) is contained in a finite union of cells (of different dimensions) embedded in an infinite-dimensional projective space, and contains the interiors of these cells. Most of the properties of the incompressible branched surfaces carrying measured laminations are preserved under the operations of splitting or passing to sub-branched surfaces.

Original languageEnglish (US)
Pages (from-to)531-573
Number of pages43
JournalTransactions of the American Mathematical Society
Volume305
Issue number2
DOIs
StatePublished - Feb 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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