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.
The µ-Invariant of 3-Manifolds and Certain Structural Properties of the Group of Homeomorphisms of a Closed, Oriented 2-Manifold, Trans
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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.