Improved stability ranges in the homology of Torelli and congruence subgroups

We improve the central stability ranges for H2(Torelli subgroup of Aut(Fn)'s) as GL_n(Z)-representations, H2(Torelli subgroup of mapping class groups) as Sp_2g(Z)-representations, Hk(congruence subgroups of GL_n®'s) as SL_n^U(R/I)-representations.