On certain fiberings of 𝑀²×𝑆¹

Heil, Wolfgang

doi:10.1090/S0002-9939-1972-0303538-3

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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