2020/11/29 by Ishibashi, Tsukasa, Kano, Shunsuke
#Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2011.14320
We give a cluster algebraic description of the reduction procedure of mapping classes along a multicurve. Based on this description, we characterize pseudo-Anosov mapping classes on a general marked surface in terms of a weaker version of the uniform sign stability, generalizing the main result in the previous paper [IK20]. Moreover we axiomatize a general reduction procedure of mutation loops parametrized by a rational polyhedral cone in the tropical cluster X-variety, which includes both the reduction along a multicurve and the cluster reduction introduced in [Ish19].