Non-uniform-perfectness conjecture for mapping class groups
Let be the mapping class group. Recall that a group is uniformly perfect if there is a natural number such that every element of is a product of at most commutators. Non-uniform-perfectness conjecture. The mapping class group is not uniformly perfect for every . The source notes that is perfect for and states that this conjecture was subsequently proved by Matsumoto and Morita, so its status is solved.
References
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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