New York Journal of Mathematics
Volume 21 (2015) 547-599


Eiko Kin

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

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Published: July 17, 2015
Keywords: Pseudo-Anosov, dilatation, topological entropy, train track representative, magic manifold, branched surface
Subject: Primary 57M27, 37E30, Secondary 37B40

We study the magic manifold N which is a hyperbolic and fibered 3-manifold. We give an explicit construction of a fiber Fa and its monodromy :Fa → Fa of the fibration associated to each fibered class a of N. Let δg (resp. δg+) 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 δ7+ and conjectural minimizers of δg for large g.


The author is supported by Grant-in-Aid for Scientific Research (C) (No. 15K04875), Japan Society for the Promotion of Science.

Author information

Department of Mathematics, Graduate School of Science, Osaka University Toyonaka, Osaka 560-0043, JAPAN