The Birman-Craggs-Johnson homomorphism is injective on the subgroup of H_k(I_g) generated by abelian cycles from disjoint separating Dehn twists, for k ≤ g-2.
The structure of the Torelli group II: A characterization of the group generated by twists on bounding curves
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Torsion in the homology of the Torelli group and the Birman-Craggs-Johnson homomorphism
The Birman-Craggs-Johnson homomorphism is injective on the subgroup of H_k(I_g) generated by abelian cycles from disjoint separating Dehn twists, for k ≤ g-2.