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The abelianization of the Johnson kernel

Alexandru Dimca, Richard Hain, Stefan Papadima (2014)

Journal of the European Mathematical Society

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 $g \geq 4$ and give an explicit presentation of it as a $S y m_{.} H_{1} (T_{g}, C)$ -module when $g \geq 6$ . 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...

Displaying 1 – 9 of 9

The abelianization of the Johnson kernel

The co-rank conjecture for 3-manifold groups.

The Finiteness Obstructions for Nilpotent Spaces lie in D (...).

The QSF property for groups and spaces.

The Schur Multipliers of SL (3, Z) and &L (4, Z).

The shape of a group---connections between shape theory and the homology of groups

The topology of the relative character varieties of a quadruply-punctured sphere.

Topological components of spaces of representations.

Two-knot groups with torsion free abelian normal subgroups of rank two.

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