On a Nielsen-Thurston classification theory for cluster modular groups

Published 21 Apr 2017 in math.GT and math.QA | (1704.06586v2)

Abstract: We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated with the corresponding cluster ensemble. The characterization gives an analogue of the Nielsen-Thurston classification theory on the mapping class group of a surface.

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Tsukasa Ishibashi

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