We show that given a collection \(X=\{f_1\), ..., \(f_m\}\) of pure mapping classes on a surface S, there is an explicit constant N, depending only on X, such that their Nth powers \(\{f_1^N\), ..., \(f_m^N\}\) generate the expected right-angled Artin subgroup of MCG(S). Moreover, we show that these subgroups are undistorted, and that each element is pseudo-Anosov on the largest possible subsurface.

中文翻译：

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在映射类组中有效生成直角artin组

我们表明，给定表面S上纯映射类的集合\（X = \ {f_1 \），...，\（f_m ​​\} \），存在一个显式常数N，仅取决于X，使得它们的N次方\（\ {f_1 ^ N \），...，\（f_m ​​^ N \} \）生成MCG（S）的预期直角Artin子组。此外，我们表明这些子组是不失真的，并且每个元素在最大可能的子表面上都是伪Anosov。