Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210585 |
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| 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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 are virtually generated by cluster Dehn twists.
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| ISSN: | 1815-0659 |