TITLE: Abelianization of mapping class groups $\Gamma_{g,n}$
QUESTION [7 upvotes]: 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)?

REPLY [9 votes]: The following statement can be found in Section 5 of Low-dimensional homology groups of mapping class groups: a survey:

Theorem: Let $g \geq 1$. Then $$H_1(\Gamma_{g,r}^n,\mathbb{Z}) \simeq \left\{ \begin{array}{cl} \mathbb{Z}_{12} & \text{if $(g,r)=(1,0)$} \\ \mathbb{Z}^r & \text{if $g=1,r \geq 1$} \\ \mathbb{Z}_{10} & \text{if $g=2$} \\ 0 & \text{if $g \geq 3$} \end{array} \right.$$

$\Gamma^n_{g,r}$ 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.