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The Quarterly Journal of Mathematics Advance Access originally published online on August 2, 2008
The Quarterly Journal of Mathematics 2009 60(4):475-486; doi:10.1093/qmath/han022
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© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

HYPERBOLIC SECTIONS IN SEIFERT-FIBERED SURFACE BUNDLES

Kazuhiro Ichihara {dagger}

School of Mathematics Education, Nara University of Education, Takabatake-cho, Nara 630-8528, Japan

Kimihiko Motegi{ddagger}

Department of Mathematics, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan

{ddagger} Corresponding author. E-mail: motegi{at}math.chs.nihon-u.ac.jp

Received 2 August 2007; revised 11 June 2008
  Abstract

Let M be a small Seifert fiber space which has also a structure of surface bundle F x [0, 1]/{(x, 0) = (f(x), 1)} over the circle, where f: F -> F is a monodromy map with non-empty fixed point set. A typical example of such a manifold appears as the result of 0-surgery on a torus knot. For each section in M, we have a ‘projection’ in F in a natural way. We give a condition assuring that the given section in M is hyperbolic in terms of the ‘projection’ in the fiber surface. By translating the result, we give a condition to obtain pseudo-Anosov automorphisms of once punctured surfaces from a periodic automorphism.

{dagger} E-mail: ichihara{at}nara-edu.ac.jp

Dedicated to Akio Kawauchi on the occasion of his 60th birthday


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