## 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