The abelianization of the Johnson kernel
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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
Publication InfoDimca, 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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Professor of Mathematics
I am a topologist whose main interests include the study of the topology of complex algebraic varieties (i.e. spaces that are the set of common zeros of a finite number of complex polynomials). What fascinates me is the interaction between the topology, geometry and arithmetic of varieties defined over subfields of the complex numbers, particularly those defined over number fields. My main tools include differential forms, Hodge theory and Galois theory, in addition to the more traditional to