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On the non-triviality of the torsion subgroup of the abelianized Johnson kernel
2022
The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves. The rational abelianization of the Johnson kernel has been computed by Dimca, Hain and Papadima, and a more explicit form was subsequently provided by Morita, Sakasai and Suzuki. Based on these results, Nozaki, Sato and Suzuki used the theory of finite-type invariants of 3-manifolds to prove that the torsion subgroup of the abelianized Johnson kernel is non-trivial. In this paper, we give a purely 2-dimensional proof of the non-triviality of this torsion subgroup and provide a lower bound for its cardinality. Our main tool is the …