Uniform bound on exponents
نویسنده
چکیده
Let S be a compact orientable surface, and Mod(S) its mapping class group. Then there exists a constant M(S), which depends on S, with the following property. Suppose a, b ∈ Mod(S) are independent (i.e., [a, b] 6= 1 for any n,m 6= 0) pseudo-Anosov elements. Then for any n,m ≥ M , the subgroup 〈a, b〉 is free of rank two, and convex-cocompact in the sense of Farb-Mosher. In particular all nontrivial elements in 〈a, b〉 are pseudo-Anosov. We also show that there exists a constant N , which depends on a, b, such that 〈a, b〉 is free of rank two and convex-cocompact if |n|+ |m| ≥ N and nm 6= 0.
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