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YCor
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index of the subgroup of the mapping class group acting trivially on Z/3Z homology

Let $S=S_g$ be the closed orientable surface of genus $g$ and let $\Gamma_3(S)$ be the subgroup of the mapping class group, $Mod(S)$, which acts trivially on $H_1(S;\mathbb{Z/3\mathbb{Z}})$. Define $\Theta(g):=[Mod(S):\Gamma_3(S)]$.

Question: Is it known if $\Theta(g)$ is exponentially large in $g$?

Mehdi Yazdi
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