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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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Strong cylindricality and the monodromy of bundles
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by Kazuhiro Ichihara, Tsuyoshi Kobayashi and Yo’av Rieck PDF
Proc. Amer. Math. Soc. 143 (2015), 3169-3176 Request permission

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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Additional Information
  • Kazuhiro Ichihara
  • Affiliation: Department of Mathematics, College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan
  • Email: ichihara@math.chs.nihon-u.ac.jp
  • Tsuyoshi Kobayashi
  • Affiliation: Department of Mathematics, Nara Women’s University, Kitauoya Nishimachi, Nara 630-8506, Japan
  • Email: tsuyoshi@cc.nara-wu.ac.jp
  • Yo’av Rieck
  • Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
  • MR Author ID: 660621
  • Email: yoav@uark.edu
  • Received by editor(s): September 12, 2013
  • Received by editor(s) in revised form: February 2, 2014
  • Published electronically: March 4, 2015
  • Additional Notes: The first author was supported by JSPS KAKENHI Grant Number 23740061.
    The second author was supported by JSPS KAKENHI Grant Number 25400091.
    This work was partially supported by a grant from the Simons Foundation (Grant Number 283495 to Yo’av Rieck).
  • Communicated by: Daniel Ruberman
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3169-3176
  • MSC (2010): Primary 57M99, 57R22
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12473-2
  • MathSciNet review: 3336641