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2020年6月19日(金) 15:00~16:00
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石橋典氏(京都大学数理解析研究所)
Algebraic entropy of sign-stable mutation loops
A mutation loop is a certain equivalence class of a sequence of mutations and permutations of indices. They form a group called the cluster modular group, which can be regarded as a combinatorial generalization of the mapping class groups of marked surfaces. We introduce a new property of mutation loops which we call the “sign stability” as a generalization of the pseudo-Anosov property of a mapping class. A sign-stable mutation loop has a numerical invariant which we call the “cluster stretch factor”, in analogy with the stretch factor of a pA mapping class. We compute the algebraic entropies of the cluster A- and X-transformations induced by a sign-stable mutation loop, and conclude that these two are estimated by the logarithm of the cluster stretch factor. This talk is based on a joint work with Shunsuke Kano.
2020年6月19日(金) 16:15~17:15
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狩野隼輔氏(東京工業大学)
Pseudo-Anosov mapping classes are sign-stable
We introduced the sign stability of mutation loops as a generalization of the pseudo-Anosov property of mapping classes of on surfaces. In this talk, I will explain the equivalence between the pseudo-Anosov property and the sign stability for a mapping class. If time permits, I will explain the relationship between the signs of mutations and train track splittings. This talk is based on a joint work with Tsukasa Ishibashi.