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Eiko Kin
Dynamics of the monodromies of the fibrations on the magic 3-manifold view print
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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 |
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Abstract
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.
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| Acknowledgements
The author is supported by Grant-in-Aid for Scientific Research (C) (No. 15K04875), Japan Society for the Promotion of Science.
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| Author information
Department of Mathematics, Graduate School of Science, Osaka University Toyonaka, Osaka 560-0043, JAPAN
kin@math.sci.osaka-u.ac.jp
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