Mapping classes associated to mixed-sign Coxeter graphs

Eriko Hironaka

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arXiv · 1110.1013

Mapping classes associated to mixed-sign Coxeter graphs

Eriko Hironaka

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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.

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BibTeX RIS

Eriko Hironaka. 2013-12-17. Mapping classes associated to mixed-sign Coxeter graphs. https://arxiv.org/abs/1110.1013

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