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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210585 |
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| 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 |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210585 |
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Ishibashi, Tsukasa 2025-12-12T10:30:46Z 2020 Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists. Tsukasa Ishibashi. SIGMA 16 (2020), 025, 22 pages 1815-0659 2020 Mathematics Subject Classification: 13F60; 05E15; 30F60 arXiv:1711.07785 https://nasplib.isofts.kiev.ua/handle/123456789/210585 https://doi.org/10.3842/SIGMA.2020.025 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. The author would like to express his gratitude to his supervisor, Nariya Kawazumi, for continuous encouragement during this work. He is very grateful to Travis Scrimshaw for pointing out an error in the presentation of Гₓ₆ in the first version of this paper. Most of the computations in this paper are done by using the Java applet for quiver mutations provided by Bernhard Keller, which is available at http://www.math.lsa.umich.edu/~fomin/cluster.html. This work is partially supported by JSPS KAKENHI Grant Number 18J13304 and the program for Leading Graduate School, MEXT, Japan. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists |
| spellingShingle |
Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists Ishibashi, Tsukasa |
| title_short |
Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists |
| title_full |
Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists |
| title_fullStr |
Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists |
| title_full_unstemmed |
Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists |
| title_sort |
presentations of cluster modular groups and generation by cluster dehn twists |
| author |
Ishibashi, Tsukasa |
| author_facet |
Ishibashi, Tsukasa |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210585 |
| citation_txt |
Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists. Tsukasa Ishibashi. SIGMA 16 (2020), 025, 22 pages |
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AT ishibashitsukasa presentationsofclustermodulargroupsandgenerationbyclusterdehntwists |
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2025-12-17T12:04:17Z |
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2025-12-17T12:04:17Z |
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1851756964601659392 |