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

作者：Kin Eiko^*

来源：The New York Journal of Mathematics, 2015, 21: 547-599.

• Pseudo-Anosov
• dilatation
• topological entropy
• train track representative
• magic manifold
• branched surface

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 -> 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.

• 出版日期2015