The abelianization of the Johnson kernel

  • Stefan Papadima

    Romanian Academy, Bucharest, Romania
  • Alexandru Dimca

    Université de Nice Sophia Antipolis, France
  • Richard Hain

    Duke University, Durham, USA


We prove that the first complex homology of the Johnson subgroup of the Torelli group is a non-trivial, unipotent -module for all and give an explicit presentation of it as a -module when . We do this by proving that, for a finitely generated group 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 . In this setup, we also obtain a precise nilpotence test.

Cite this article

Stefan Papadima, Alexandru Dimca, Richard Hain, The abelianization of the Johnson kernel. J. Eur. Math. Soc. 16 (2014), no. 4, pp. 805–822

DOI 10.4171/JEMS/447