A note on the abelianizations of finite-index subgroups of the mapping   class group
  For some $g \geq 3$, let $\Gamma$ be a finite index subgroup of the mapping class group of a genus $g$ surface (possibly with boundary components and punctures). An old conjecture of Ivanov says that the abelianization of $\Gamma$ should be finite. In this note, we prove two theorems supporting this conjecture. For the first, let $T_x$ denote the Dehn twist about a simple closed curve $x$. For some $n \geq 1$, we have $T_x^n \in \Gamma$. We prove that $T_x^n$ is torsion in the abelianization of $\Gamma$. Our second result shows that the abelianization of $\Gamma$ is finite if $\Gamma$ contains a "large chunk" (in a certain technical sense) of the Johnson kernel, that is, the subgroup of the mapping class group generated by twists about separating curves. This generalizes work of Hain and Boggi. 
Andrew Putman