Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists

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dc.contributor.authorIshibashi, Tsukasa
dc.date.accessioned2025-12-12T10:30:46Z
dc.date.issued2020
dc.description.abstractWe 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.
dc.description.sponsorshipThe 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.
dc.identifier.citationPresentations of Cluster Modular Groups and Generation by Cluster Dehn Twists. Tsukasa Ishibashi. SIGMA 16 (2020), 025, 22 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.025
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 13F60; 05E15; 30F60
dc.identifier.otherarXiv:1711.07785
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210585
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titlePresentations of Cluster Modular Groups and Generation by Cluster Dehn Twists
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік