The rational abelianization of the Chillingworth subgroup is given by the first Johnson homomorphism and the Casson-Morita homomorphism as a mapping class group module.
Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math
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The rational abelianization of the Chillingworth subgroup of the mapping class group of a surface
The rational abelianization of the Chillingworth subgroup is given by the first Johnson homomorphism and the Casson-Morita homomorphism as a mapping class group module.