The abelianization of the Johnson kernel
| dc.contributor.author | Dimca, A | |
| dc.contributor.author | Hain, R | |
| dc.contributor.author | Papadima, S | |
| dc.date.accessioned | 2014-07-29T16:58:04Z | |
| dc.date.issued | 2014-01-01 | |
| dc.description.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(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. | |
| dc.identifier.issn | 1435-9855 | |
| dc.identifier.uri | ||
| dc.publisher | European Mathematical Society Publishing House | |
| dc.relation.ispartof | Journal of the European Mathematical Society | |
| dc.relation.isversionof | 10.4171/JEMS/447 | |
| dc.title | The abelianization of the Johnson kernel | |
| dc.type | Journal article | |
| duke.contributor.orcid | Hain, R|0000-0002-7009-6971 | |
| pubs.begin-page | 805 | |
| pubs.end-page | 822 | |
| pubs.issue | 4 | |
| pubs.organisational-group | Duke | |
| pubs.organisational-group | Mathematics | |
| pubs.organisational-group | Trinity College of Arts & Sciences | |
| pubs.publication-status | Published | |
| pubs.volume | 16 |
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