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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Measured laminations in $3$-manifolds
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by Ulrich Oertel PDF
Trans. Amer. Math. Soc. 305 (1988), 531-573 Request permission

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 ${\pi _1}$. There is a space $\mathcal {P}\mathcal {L}(M)$ whose points are projective classes of essential measured laminations. Projective classes of weighted incompressible surfaces are dense in $\mathcal {P}\mathcal {L}(M)$. The space $\mathcal {P}\mathcal {L}(M)$ 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.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 305 (1988), 531-573
  • MSC: Primary 57M99
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0924769-1
  • MathSciNet review: 924769