Mapping classes associated to mixed-sign Coxeter systems

Eriko Hironaka

Given an ordered fat graph with labeled vertices we define a generalized Coxeter system, and Coxeter element. We then construct an associated mapping class with the property that its image under the symplectic homomorphism is conjugate to the negative of the Coxeter element. Applying a result of Lanneau and Thiffeault, we show that the minimum dilatations for orientable pseudo-Anosov mapping classes of surfaces with small genus can be realized by mapping classes of this form.