We show that if is a cocommutative Hopf algebra, then there is a natural action of on which induces an action on a quotient . In the case when is the tensor algebra, we show that the invariant of the cokernel of the Johnson homomorphism studied in Algebr. Geom. Topol. 15 (2015) 801–821 projects to take values in . We analyze the case, getting large families of obstructions generalizing the abelianization obstructions of Geom. Dedicata 176 (2015) 345–374.
"Hopf algebras and invariants of the Johnson cokernel." Algebr. Geom. Topol. 16 (4) 2325 - 2363, 2016. https://doi.org/10.2140/agt.2016.16.2325