We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
The abelianization of the Johnson kernel.
- Authors
Dimca, Alexandru; Hain, Richard; Papadima, Stefan
- Abstract
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(T_g,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.
- Subjects
TORELLI theorem; HOMOLOGY theory; POLYNOMIALS; LIE algebras; ARITHMETIC
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2014, Vol 16, Issue 4, p805
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/447