The abelianization of the Johnson kernel
Journal Article
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.
Full Text
Duke Authors
Cited Authors
- Dimca, A; Hain, R; Papadima, S
Published Date
- January 1, 2014
Published In
Volume / Issue
- 16 / 4
Start / End Page
- 805 - 822
International Standard Serial Number (ISSN)
- 1435-9855
Digital Object Identifier (DOI)
- 10.4171/JEMS/447
Citation Source
- Scopus