Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2020
• Автор: Ishibashi, Tsukasa
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2020
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/210585
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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...