Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Author: Ishibashi, Tsukasa
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210585
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists. Tsukasa Ishibashi. SIGMA 16 (2020), 025, 22 pages

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 X₆ and X₇. We verify that the cluster modular groups of finite mutation type Ẽ₆, Ẽ₇, Ẽ₈, G⁽*'*⁾₂, X₆ and X₇ a...