Quotient families of mapping classes

Abstract

Thurston's fibered face theory allows us to partition the set of pseudo-Anosov mapping classes on different compact oriented surfaces into subclasses with related dynamical behavior. This is done via a correspondence between the rational points on fibered faces in the first cohomology of a hyperbolic 3-manifold and the monodromies of fibrations of the 3-manifold over the circle. In this paper, we generalize examples of Penner, and define quotient families of mapping classes. We show that these mapping classes correspond to open linear sections of fibered faces. The construction gives a simple way to produce families of pseudo-Anosov mapping classes with bounded normalized dilatation and computable invariants, and gives concrete examples of mapping classes associated to sequences of points tending to the interior and to the boundary of fibered faces.

This paper has been corrected and revised. It will appear in Topology Proceedings

References in corpus (5)

• A family of pseudo-Anosov braids with small dilatation
• Small dilatation pseudo-Anosov mapping classes coming from the simplest hyperbolic braid
• Small dilatation pseudo-Anosovs and 3-manifolds
• Sequences of pseudo-Anosov mapping classes and their asymptotic behavior
• Mapping classes associated to mixed-sign Coxeter graphs

Cited by in corpus (5)

• Statistics of Random 3-Manifolds occasionally fibering over the circle
• Dynamics of the monodromies of the fibrations on the magic 3-manifold
• A Proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus
• An upper bound on the asymptotic translation lengths on the curve graph and fibered faces
• The asymptotic behavior of the minimal pseudo-Anosov dilatations in the hyperelliptic handlebody groups