Let $S\_{g,n}$ be a Riemann surface of genus $g$, with $n$ points removed. The mapping class group of $S\_{g,n}$ is denoted by $\Gamma\_{g,n}$. 


Is there a reference where the abelianization of $\Gamma\_{g,n}$ calculated (or at least for $g$ sufficiently large, are they trivial)?



Abelianization of mapping class groups $\Gamma_{g,n}$
The following statement can be found in Section 5 of [Low-dimensional homology groups of mapping class groups: a survey](https://arxiv.org/abs/math/0307111):



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> **Theorem:** Let $g \geq 1$. Then $$H\_1(\Gamma\_{g,r}^n,\mathbb{Z}) \simeq \left\{ \begin{array}{cl} \mathbb{Z}\_{12} & \text{if $(g,r)=(1,0)$} \\ \mathbb{Z}^r & \text{if $g=1,r \geq 1$} \\ \mathbb{Z}\_{10} & \text{if $g=2$} \\ 0 & \text{if $g \geq 3$} \end{array} \right.$$
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$\Gamma^n\_{g,r}$ denotes the mapping class group of a connected orientable surface of genus $g$ with $r$ boundary components and $n$ punctures. Precise references are given in the survey.


