TITLE: Second homology of mapping class group of genus 3
QUESTION [8 upvotes]: In a survey paper of Korkmaz it is stated that $H_2(\mathrm{Mod}_3)$ is either $\Bbb Z$ or $\Bbb Z \oplus \Bbb Z_2$, but I was not able to find out a precise computation of this group (resolving the ambiguity). Is this group known? Any reference?

REPLY [11 votes]: In his paper "Lagrangian mapping class groups from a group homological point of view" (available here), Sakasai proves that the desired homology group is $\mathbb{Z} \oplus \mathbb{Z}/2$.