Geodesic
The abelianization of the Johnson kernel
Journal of the European Mathematical Society, Tome 16 (2014) no. 4, pp. 805-822

Voir la notice de l'article provenant de la source EMS Press

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∙​H1​(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.
DOI : 10.4171/jems/447
Classification : 20-XX, 16-XX, 55-XX, 57-XX
Keywords: Torelli group, Johnson kernel, Malcev completion, I-adic completion, characteristic variety, support, nilpotent module, arithmetic group, associated graded Lie algebra, infinitesimal Alexander invariant 
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     title = {The abelianization of the {Johnson} kernel},
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Alexandru Dimca; Richard Hain; Stefan Papadima. The abelianization of the Johnson kernel. Journal of the European Mathematical Society, Tome 16 (2014) no. 4, pp. 805-822. doi: 10.4171/jems/447

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