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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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On the construction of branched coverings of low-dimensional manifolds
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by Israel Berstein and Allan L. Edmonds PDF
Trans. Amer. Math. Soc. 247 (1979), 87-124 Request permission

Abstract:

Several general results are proved concerning the existence and uniqueness of various branched coverings of manifolds in dimensions 2 and 3. The results are applied to give a rather complete account as to which 3-manifolds are branched coverings of ${S^3}$, ${S^2} \times {S^1}$, ${P^2} \times {S^1}$, or the nontrivial ${S^3}$-bundle over ${S^1}$, and which degrees can be achieved in each case. In particular, it is shown that any closed nonorientable 3-manifold is a branched covering of ${P^2} \times {S^1}$ of degree which can be chosen to be at most 6 and with branch set a simple closed curve. This result is applied to show that a closed nonorientable 3-manifold admits an open book decomposition which is induced from such a decomposition of ${P^2} \times {S^1}$.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 247 (1979), 87-124
  • MSC: Primary 57M10
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0517687-9
  • MathSciNet review: 517687