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Proceedings of the American Mathematical Society

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

 

 

On certain fiberings of $ M\sp{2}\times S\sp{1}$


Author: Wolfgang Heil
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1972-0303538-3
Keywords: Fiberings of 3-manifolds over $ {S^1}$, Seifert fiber space, Nielsen invariants for surfaces
Article copyright: © Copyright 1972 American Mathematical Society