Mapping classes associated to mixed-sign Coxeter graphs

2011/10/05 by Eriko Hironaka, Hironaka, Eriko · 1 citation
Mathematics · #20F55 #37E30 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1110.1013

openalex publication_date 2011/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Die Gruppe der Abbildungsklassen: Das arithmetische Feld auf Flächen
• Small dilatation pseudo-Anosovs and 3-manifolds
• Sequences of pseudo-Anosov mapping classes and their asymptotic behavior

Cited by

• A Proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus

Related

• On generating mapping class groups by pseudo-Anosov elements
• Normal generators for mapping class groups are abundant
• Chordal Coxeter Groups
• Sequences of pseudo-Anosov mapping classes and their asymptotic behavior
• Simply-laced mixed-sign Coxeter groups, with an associate graph is a line or a simple cycle