The abelianization of the Johnson kernel

Journal Article (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