Mapping classes associated to mixed-sign Coxeter graphs

Details Mapping classes associated to mixed-sign Coxeter graphs Mapping classes associated to mixed-sign Coxeter graphs

2011-10-05

arxiv.org/abs/1110.1013v1

Mathematics

Geometric Topology

16 pages, 13 figures

Scientific paper

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 mapping classes for surfaces of small genus can be realized by mapping classes of this form.

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