Publications [#287267] of Richard Hain

Papers Published

1. Dimca, A; Hain, R; Papadima, S, The abelianization of the Johnson kernel, Journal of the European Mathematical Society, vol. 16 no. 4 (January, 2014), pp. 805-822, ISSN 1435-9855 [arXiv:1101.1392], [1392], [doi]
   (last updated on 2025/04/05)

   Abstract:
   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.