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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On certain fiberings of $M^{2}\times S^{1}$
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by Wolfgang Heil PDF
Proc. Amer. Math. Soc. 34 (1972), 280-286 Request permission

Abstract:

Using a theorem of Stallings it is shown that the product of ${S^1}$ and a surface of genus $g > 1$ admits for every integer $n \geqq 0$ a fibering over ${S^1}$ with a surface of genus $n(g - 1) + g$ as fiber. Conversely, these are all possible such fibrations (up to equivalence). Let N be a Seifert fiber space which is locally trivial fibered over ${S^1}$ with fiber a surface. It is shown that any two such fiberings of N over ${S^1}$ are equivalent if the fibers are homeomorphic.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 280-286
  • MSC: Primary 55F05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0303538-3
  • MathSciNet review: 0303538