Non-uniform-perfectness conjecture for mapping class groups
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.
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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