The abelianization of the Johnson kernel
Stefan Papadima
Romanian Academy, Bucharest, RomaniaAlexandru Dimca
Université de Nice Sophia Antipolis, FranceRichard Hain
Duke University, Durham, USA
Abstract
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