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arXiv · 1711.07785

Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists

Tsukasa Ishibashi
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Abstract

We give a method to compute presentations of saturated cluster modular groups. Using this, we obtain finite presentations of the saturated cluster modular groups of finite mutation type $X_6$ and $X_7$. We verify that the cluster modular groups of finite mutation type $\widetilde{E}_6$, $\widetilde{E}_7$, $\widetilde{E}_8$, $G_2^{(*,*)}$, $X_6$ and $X_7$ are virtually generated by cluster Dehn twists.

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Tsukasa Ishibashi. 2017-11-21. Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists. https://doi.org/10.3842/sigma.2020.025

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