Dynamics of the monodromies of the fibrations on the magic 3-manifold

Abstract

We study the magic manifold $N$ which is a hyperbolic and fibered $3$-manifold. We give an explicit construction of a fiber $F_a$ and its monodromy $:F_a\to F_a$ of the fibration associated to each fibered class $a$ of $N$. Let ${\delta }_g$ (resp. ${\delta }_g^{+}$) be the minimal dilatation of pseudo-Anosovs (resp. pseudo-Anosovs with orientable invariant foliations) defined on an orientable closed surface of genus $g$. As a consequence of our result, we obtain the first explicit construction of the following pseudo-Anosovs; a minimizer of ${\delta }_7^{+}$ and conjectural minimizers of ${\delta }_g$ for large $g$.

arXiv comment46 pages, 36 figures

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Cited by in corpus (3)

• Small asymptotic translation lengths of pseudo-Anosov maps on the curve complex
• A construction of pseudo-Anosov braids with small normalized entropies
• The asymptotic behavior of the minimal pseudo-Anosov dilatations in the hyperelliptic handlebody groups