On the structure of the top homology group of the Johnson kernel

The Johnson kernel is the subgroup Kg of the mapping class group Mod(Eg) of a genus-g oriented closed surface E g generated by all Dehn twists about separating curves. We study the structure of the top homology group H 2g _ 3 ( K g , Z). For any collection of 2g- 3 disjoint separating curves on E g , one can construct the corresponding abelian cycle in the group H 2g _ 3 ( K g , Z); such abelian cycles will be called simple. We describe the structure of a Z[Mod(Eg)RKg]-module on the subgroup of H 2g _ 3 ( K g , Z) generated by all simple abelian cycles and find all relations between them.