The abelianization of the Johnson kernel
Dimca, A
Hain, R
Papadima, S
We prove that the first complex homology of the Johnson subgroup of the Torelli group Tg is a non-trivial, unipotent Tg-module for all g ≥ 4 and give an explicit presentation of it as a Sym H 1(Tg,C)-module when g ≥ 6. We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the infinitesimal Alexander invariant of the associated graded Lie algebra of G. In this setup, we also obtain a precise nilpotence test. © European Mathematical Society 2014.
Published Version (Please cite this version)
10.4171/JEMS/447
Dimca, A; Hain, R; & Papadima, S (2014). The abelianization of the Johnson kernel. Journal of the European Mathematical Society, 16(4). pp. 805-822. 10.4171/JEMS/447. Retrieved from https://hdl.handle.net/10161/8975.
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