The abelianization of the Johnson kernel

Dimca, Alexandru, Hain, Richard, and Papadima, Stefan. "The abelianization of the Johnson kernel." Journal of the European Mathematical Society 016.4 (2014): 805-822. <http://eudml.org/doc/277466>.

@article{Dimca2014,
abstract = {We prove that the first complex homology of the Johnson subgroup of the Torelli group $T_g$ is a non-trivial, unipotent $T_g$-module for all $g\ge 4$ and give an explicit presentation of it as a $Sym_\{.\} H_1(T_g,C)$-module when $g\ge 6$. 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.},
author = {Dimca, Alexandru, Hain, Richard, Papadima, Stefan},
journal = {Journal of the European Mathematical Society},
keywords = {Torelli group; Johnson kernel; Malcev completion; $I$-adic completion; characteristic variety; support; nilpotent module; arithmetic group; associated graded Lie algebra; infinitesimal Alexander invariant; Torelli group; Johnson kernel; Malcev completion; -adic completion; characteristic variety; support; nilpotent module; arithmetic group; associated graded Lie algebra; infinitesimal Alexander invariant},
language = {eng},
number = {4},
pages = {805-822},
publisher = {European Mathematical Society Publishing House},
title = {The abelianization of the Johnson kernel},
url = {http://eudml.org/doc/277466},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Dimca, Alexandru
AU - Hain, Richard
AU - Papadima, Stefan
TI - The abelianization of the Johnson kernel
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 4
SP - 805
EP - 822
AB - We prove that the first complex homology of the Johnson subgroup of the Torelli group $T_g$ is a non-trivial, unipotent $T_g$-module for all $g\ge 4$ and give an explicit presentation of it as a $Sym_{.} H_1(T_g,C)$-module when $g\ge 6$. 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.
LA - eng
KW - Torelli group; Johnson kernel; Malcev completion; $I$-adic completion; characteristic variety; support; nilpotent module; arithmetic group; associated graded Lie algebra; infinitesimal Alexander invariant; Torelli group; Johnson kernel; Malcev completion; -adic completion; characteristic variety; support; nilpotent module; arithmetic group; associated graded Lie algebra; infinitesimal Alexander invariant
UR - http://eudml.org/doc/277466
ER -