Dynamics of the monodromies of the fibrations on the magic 3-manifold (Q887771)

In this paper, the author studies the so-called \textit{magic manifold}. This is a fibered hyperbolic manifold with pseudo-Anosov monodromy. Topologically, it is the exterior of the 3-chain link \(\mathcal{C}_3\). For each integral fibered class in homology (referring to the definition of Thurston's norm), explicit constructions of a fiber and of a monodromy map are obtained. Examining the dynamics of such a monodromy, an explicit construction of pseudo-Anosov maps is given, together with an estimate of their dilatation. The author contributes to the question of finding the minimal pseudo-Anosov dilatation on surfaces of genus \(7\). The paper also contains a result on the asymptotic behavior of pseudo-Anosov minimal dilatations, for surfaces of genus \(g\geq 2\) under some conditions on \(g\). The proofs use the technique of train tracks.