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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Bibliographic Details
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
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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
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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.
ISSN:1815-0659