Let $S_g$ be a closed surface of genus $g\geq 2$. Given $r \in \mathbb{N}$, what is the number of elements of order $r$ in the mapping class group? Is it finite or infinite? If it is infinite is there any way to generate such a class? If it is finite is there an upper bound on the number? Any reference of link will be extremely helpful. Thanks in advance.
2026-04-03 19:37:52.1775245072
Number of fixed order elements in the mapping class group of a closed surface
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