Torelli group

The Torelli group $ I_g$ is the subgroup of the mapping class group $ \Gamma_g$ that acts trivially on the first homology of the surface $ F_g$. It is the kernel of the map $ \Gamma_g \rightarrow
Sp(2g,\mathbb{Z})$ and captures (in some sense) the difference between the topology of $ \mathcal{M}_g$ and that of $ \mathcal{A}_g$, the moduli space of principally polarized abelian varieties

Jeffrey Herschel Giansiracusa 2005-06-27