The kernel of the Birman-Craggs-Johnson homomorphism

Abstract

For surfaces of genus $g\ge 3$ 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.

33 pages, 13 figures