Strong cylindricality and the monodromy of bundles

Kazuhiro Ichihara; Tsuyoshi Kobayashi; Yo'av Rieck

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arXiv · 1309.3165

Strong cylindricality and the monodromy of bundles

Kazuhiro Ichihara·Tsuyoshi Kobayashi·Yo'av Rieck

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Abstract

A surface $F$ in a 3-manifold $M$ is called cylindrical if $M$ cut open along $F$ admits an essential annulus $A$. If, in addition, $(A, \partial A)$ is embedded in $(M, F)$, then we say that $F$ is strongly cylindrical. Let $M$ be a connected 3-manifold that admits a triangulation using $t$ tetrahedra and $F$ a two-sided connected essential closed surface of genus $g(F)$. We show that if $g(F)$ is at least $38 t$, then $F$ is strongly cylindrical. As a corollary, we give an alternative proof of the assertion that every closed hyperbolic 3-manifold admits only finitely many fibrations over the circle with connected fiber whose translation distance is not one, which was originally proved by Saul Schleimer.

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BibTeX RIS

Kazuhiro Ichihara, Tsuyoshi Kobayashi, Yo'av Rieck. 2014-03-10. Strong cylindricality and the monodromy of bundles. https://arxiv.org/abs/1309.3165

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