The kernel of the Birman-Craggs-Johnson homomorphism
Tara E. Brendle, Dan Margalit, Andrew Putman
Abstract
For surfaces of genus g ≥ 3 with at most one boundary component, we give explicit generating sets for the kernel of the Birman-Craggs-Johnson homomorphism and the commutator subgroup of the Torelli group. As an application, we give a new proof of Johnson's calculation of the abelianization of the Torelli group.
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