Non-uniform-perfectness conjecture for mapping class groups

Let Mg{\cal M}_g be the mapping class group. Recall that a group Γ{\varGamma} is uniformly perfect if there is a natural number NN such that every element of Γ{\varGamma} is a product of at most NN commutators. Non-uniform-perfectness conjecture. The mapping class group Mg{\cal M}_g is not uniformly perfect for every g3g\geq 3. The source notes that Mg{\cal M}_g is perfect for g3g\geq 3 and states that this conjecture was subsequently proved by Matsumoto and Morita, so its status is solved.

Sources & referencesView supporting material

Primary source

Shigeyuki Morita, “Structure of the mapping class groups of surfaces: a survey and a prospect”, arXiv:math/9911258 (1999).

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