Mapping classes associated to mixed-sign Coxeter graphs

Abstract

We define a generalization of Coxeter graphs and an associated Coxeter system and Coxeter mapping class. These can be used to construct periodic Coxeter mapping classes on surfaces with arbitrarily large genus, preserving lots of symmetries. The periodic mapping classes can in turn be used to construct sequences of pseudo-Anosov mapping classes with bounded normalized dilatation and arbitrarily high genus. We show that the smallest known accumulation point of normalized dilatations can be realized by such a sequence.

38 pages, 38 figures. Exposition improved, figures added

References in corpus (4)

• 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

Cited by in corpus (5)

• Quotient families of mapping classes
• 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
• On Coxeter mapping classes and fibered alternating links
• Small dilatation homeomorphisms as monodromies of Lorenz knots